Lectures on the electromagnet

UC-NRLF

HS

GIFT OF
Prof .E.P.Lewis

J

LECTUEES

THE ELECTROMAGNET

BY

SILVANUS P. THOMPSON, D.Sc., B.A., F.R.A.S.

PRINCIPAL OF, AND PROFESSOR OF PHYSICS IN THE CITY AND GUILDS

OF LONDON TECHNICAL COLLEGE, FINSBURY ; VICE PRESIDENT

OF THE PHYSICAL SOCIETY OF LONDON, ETC., ETC.

AUTHORIZED AMERICAN EDITION

NEW YORK:
THE W. J. JOHNSTON COMPANY, LTD.

1891.

NOTICE.

This course of four Lectures on the Electromagnet
was delivered in February, 1890, before the Society of
Arts, London, and constituted one of the sets of " Can-
tor" Lectures of the Session 1889-90. This volume is
reprinted with the direct sanction of the Author, who
has revised the text for republication. It is the only
authorized American edition.

y

PHYSICS DEPT.

/-/? Ztcvz-

CONTENTS.

PAGE

LECTURE L, 7

Introductory ; Historical Sketch ; Generalities Concerning Electro-
magnets ; Typical Forms ; Polarity ; Uses in General ; The Proper-
ties of Iron; Methods of Measuring Permeability; Traction Methods;
Curves of Magnetization and Permeability; The Law of the Electro-
magnet; Hysteresis; Fallacies arid Facts about Electromagnets.

LECTURE II., 80

General Principles of Design and Construction ; Principles of the
Magnetic Circuit.

APPENDIX TO LECTURE II., 161

Calculation of Excitation, Leakage, etc. ; Rules for Estimating Magnetic
Leakage.

LECTURE III., 171

Special Designs; Winding of the Copper; Windings for Constant
Pressure and for Constant Current ; Miscellaneous Rules about
Winding; Specifications of Electromagnets; Amateur Rule about
Resistance of Electromagnet and Battery; Forms of Electromagnets;
Effect of Size of Coils ; Effect of Position of Coils ; Effect of Shape
of Section; Effect of Distance between Poles ; Researches of Prof .
Hughes; Position and Form of Armature; Pole-Pieces on -Horse-
shoe Magnets ; Contrasts between Electromagnets and Permanent
Magnets; Electromagnets for Maximum Traction; Electromagnets
for Maximum Range of Attraction ; Electromagnets of Minimum
Weight ; A Useful Guiding Principle ; Electromagnets for Use with
Alternating Currents ; Electromagnets for Quickest Action ; Con-
necting Coils for Quickest Action ; Battery Grouping for Quickest
Action ; Time-Constant of Electromagnets ; Short Cores vs. Long
Cores.

LECTURE IV 222

Electromagnetic Mechanism ; The Coil-and-Plunger; Effect of Using
Coned Plunger ; Other Modes of Extending Range of Action; Modi-
fications of the Coil-and-Plunger ; Differential Coil-and-Plunger ;
Coil-and-Plunger Coil ; Intermediate Forms ; Action of Magnetic
Field on Small Iron Sphere; Sectioned Coils with Plunger; Winding
of Tubular Coils and Electromagnets ; Extension of Range by Oblique
Approach ; Polarized Mechanism ; Uses of Permanent Magnets ;
Electromagnetic Mechanism; Moving Coil in Permanent Magnetic
Field; Magnetic Adherence; Repulsion Mechanism; Electromag-
netic Vibrators ; Indicator Movements ; The Study of Electromag-
netic Mechanism; Suppression of Sparking; Conclusion,

f, * m* t*V rv *

557i)Ji4

LIST OF ILLUSTRATIONS.

PAGE

Sturgeon's First Electromagnet, 18

Sturgeon's Straight-Bar Electromagnet, 19

Sturgeon's Lecture-Table Electromagnet, 25

Henry's Electromagnet, . 35

Henry's Experimental Electromagnet, 36

Joule's Electromagnet, 41

Joule's Cylindrical Electromagnet, 45

Roberts' Electromagnet, 46

Joule's Zigzag Electromagnet, *. 46

Typical Two-Pole Electromagnet, 50

Iron-Clad Electromagnet, 50

Diagram Illustrating Relation of Magnetizing Circuit and Resulting

Magnetic Force, 51

Curves of Magnetization of Different Magnetic Materials, . . . .57

Ring Method of Measuring Permeability (Rowland's Arrangement), . 60

Bosanquet's Data of Magnetic Properties of Iron and Steel Rings, . . 62

Hopkinson's Divided Bar Method of Measuring Magnetic Permeability, 64

Curves of Magnetization of Iron, 66

The Permeameter, 70

Curves of Permeability, 73

Curves of Hysteresis, 75

Bosanquet's Verification of the Law of Traction, 90

Stumpy Electromagnet, 97

Experiment on Rounding Ends, 105

Experiment of Detaching Armature, 105

Lines of Force Running through Bar Magnet, 107

Apparatus to Illustrate the Law of Inverse Squares, 113

Deflection of Needle Caused by Bar Magnet Broadside on, . . .115

Closed Magnetic Circuit, 116

Divided Magnetic Circuit, 117

Electromagnet with Armature in Contact, 119

Electromagnet with Air-Gaps One Millimetre Wide, 119

Electromagnet with Air-Gaps Several Millimetres Wide, . . . .121

Electromagnet without Armature, .,,,,,, , , 131

LIST OF ILLUSTRATIONS. 5

PAGtE

Contrasted Effect of Flat and Pointed Poles, 127

Dub's Experiments with Pole- Pieces, 129

Dub's Deflection Experiment, 130

Deflecting a Steel Magnet Having Bifilar Suspension Pole-Piece on

Near End 131

Deflecting Steel Magnet Pole-Piece on Distant End, . . 131

Experiment with Tubular Core and Iron Ring, .

Exploring Polar Distribution with Small Iron Ball, . ... 137

Iron Ball Attracted to Edge of Polar Face, 139

Experiment on Leakage of Electromagnet, ... . 140

Curves of Magnetization Plotted from Preceding, 143

Curves of Flow of Magnetic Lines in Air from One Cylindrical Pole to

Another, 146

Diagram of Leakage Reluctances, 148

Von Feilitzsch's Curves of Magnetization of Rods of Various Diameters, 152

Ewing's Curves for Effect of Joints, 157

Von Feilitzsch's Curves of Magnetization of Tubes, 159

Club-Footed Electromagnet, 189

Hughes' Electromagnet, . 195

Experiment with Permanent Magnet, 200

Electromagnetic Pop-Gun, 205

Curves of Rise of Currents 211

Curves of Rise of Current with Different Groupings of Battery, . .216

Electromagnets of Relay and their Effects, 219

Hjorth's Electromagnetic Mechanism, 224

Action of Single Coil on Point Pole on Axis, 230

Action along Axis of Single Coil, 230

Action of Tubular Coil, 232

Diagram of Force and Work of Coil-and-Plunger, 235

Von Feilitzsch's Experiment on Plungers of Iron and Steel, . . .244

Bruger's Experiments on Coils and Plungers, ...... 245

Bruger's Experiments, Using Currents of Various Strengths, . . .245

Plunger Electromagnet of Stevens and Hardy, 252

Electromagnet of Brush Arc Lamp, 253

Ayrton and Perry's Tubular Iron-Clad Electromagnet, . . . .254

Froment's Equalizer with Stanhope Lever 261

Davy's Mode of Controlling Armature by Spring 261

Robert Houdin's Equalizer, 262

Mechanism of Duboscq's Arc Lamp, 263

Nickles' Magnetic Friction Gear, 271

Forbes' Electromagnet, 272

Electromagnetic Mechanism Working by Repulsion, 273

Repulsion between Two Parallel Cores 273

THE

ELECTROMAGNET.

LECTURE T.

INTRODUCTORY.

AMONG the great inventions which have originated in
the lecture-room in which we are met are two of special
interest to electricians the application of gutta-percha
to the purpose of submarine telegraph cables, and the
electromagnet. This latter invention was first publicly
described, from the very platform on which I stand, on
May 23, 1825, by William Sturgeon, whose paper is to
be found in the forty-third volume of the Transactions
of the Society of Arts. For this invention we may right-
fully claim the very highest place. Electrical engineer-
ing, the latest and most vigorous offshoot of applied
science, embraces many branches. The dynamo for
generating electric currents, the motor for transforming
their energy back into work, the arc lamp, the electric
bell, the telephone, the recent electromagnetic machin-
ery for coal-mining, for the separation of ore, and many

LK(TntI->: ON THE ELECTROMAGNET.

other electro-mechanical contrivances, come within the
purview of the electrical engineer. In every one of
these, and in many more of the useful applications of
electricity, the central organ is an electromagnet. By
means of this simple and familiar contrivance an iron
core surrounded by a copper-wire coil mechanical ac-
tions are produced at will, at a distance, under control,
by the agency of electric currents. These mechanical
actions are known to vary with the mass, form, and
quality of the iron core, the quantity and disposition
of the copper wire wound upon it, the quantity of
electric current circulating around it, the form, quality,
and distance of the iron armature upon which it aces.
But the laws which govern the mechanical action in re-
lation to these various matters are by no means well
known, and, indeed, several of them have long been a
matter of dispute. Gradually, however, that which has
been vague and indeterminate becomes clear and pre-
cise. The laws of the steady circulation of electric cur-
rents, at one time altogether obscure, were cleared up
by the discovery of the famous law of Ohm. Their ex-
tension to the case of rapidly interrupted currents, such
as are used in telegraphic working, was discovered by
Helmholtz; while to Maxwell is due their future exten-
sion to alternating, or, as they are sometimes called,
undulatory currents. All this was purely electric work.
But the law of the electromagnet was still undiscovered;
the magnetic part of the problem was still buried in
obscurity. The only exact reasoning about magnetism
dealt with problems of another kind; it was couched in
language of a misleading character; for the practical

LECTURES ON THE ELECTROMAGNET. 9

problems connected with the electromagnet it was worse
than useless. The doctrine of two magnetic fluids dis-
tributed over the end surfaces of magnets, under the
sanction of the great names of Coulomb, of Poisson,
and of Laplace, had unfortunately become recognized
as an accepted part of science along with the law of in-
verse squares. How greatly the progress of electromag-
netic science has been impeded and retarded by the
weight of these great names it is impossible now to
gauge. We now know that for all purposes, save only
those whose value lies in the domain of abstract mathe-
matics, the doctrine of the two magnetic fluids is false
and misleading. We know that magnetism, so far from
residing on the end or surface of the magnet, is a prop-
erty resident throughout the mass; that the internal,
not the external, magnetization is the important fact to
be considered; that the so-called free magnetism on the
surface is, as it were, an accidental phenomenon; that
the magnet is really most highly magnetized at those
parts where there is least surface magnetization; finally,
that the doctrine of surface distribution of fluids is ab-
solutely incompetent to afford a basis of calculation such
as is required by the electrical engineer. He requires
rules to enable him not only to predict the lifting power
of a given electromagnet, but also to guide him in de-
signing and constructing electromagnets of special forms
suitable for the various cases that arise in his practice.
He wants in one place a strong electromagnet to hold
on to its armature like a limpet to its native rock ; in
another case he desires a magnet having a very long
range of attraction, and wants a rule to guide him to

10 LECTURES ON THE ELECTROMAGNET.

the best design; in another he wants a special form
having the most rapid action attainable; in yet another
he must sacrifice everything else to attain maximum
action with minimum weight. Toward the solution of
such practical problems as these the old theory of mag-
netism offered not the slightest aid. Its array of math-
ematical symbols was a mockery. It was as though an
engineer asking for rules to enable him to design the
cylinder and piston of an engine were confronted with
recipes how to estimate the cost of painting it.

Gradually, however, new light dawned. It became
customary, in spite of the mathematicians, to regard the
magnetism of a magnet as something that traverses or
circulates around a definite path, flowing more freely
through such substances as iron than through other
relatively non-magnetic materials. Analogies between
the flow of electricity in an electrically conducting cir-
cuit, and the passage of magnetic lines of force through
circuits possessing magnetic conductivity, forced them-
selves upon the minds of experimenters, and compelled
a mode of thought quite other than that previously ac-
cepted. So far back as 1821, Gumming 1 experimented
on magnetic conductivity. The idea of a magnetic
circuit was more or less familiar to Ritchie, 2 Sturgeon, 3
Dove, 4 Dub, 5 and De La Rive, 6 the last-named of whom

1 Camb. Phil. Trans., Apr. 2, 1821.

2 Phil. Mag., series iii., vol. iii., p. 122.
a Ann. ofElectr., xii., p. 217.

* Pogg. Ann., xxix., p. 462, 1833. See aiso Pogg. Ann., xliii., p. 517, 1838.

5 Dub, " Elektromagnetismus " (ed. 1861), p. 401 ; and Pogg. Ann., xc., p.
440, 1853.

8 De La Rive, " Treatise on Electricity" (Walker's translation), vol. i., p.
292.

LECTURES ON THE ELECTROMAGNET. 11

explicitly uses the phrase, " a closed magnetic circuit."
Joule 7 found the maximum power of an electromagnet
to be proportional to " the least sectional area of the en-
tire magnetic circuit," and he considered the resistance
to induction as proportional to the length of the mag-
netic circuit. Indeed, there are to be found scattered
in Joule's writings on the subject of magnetism, some
five or six sentences, which, if collected together, consti-
tute a very full statement of the whole matter. Fara-
day 8 considered that he had proved that each magnetic
line of force constitutes a closed curve; that the path of
these closed curves depended on the magnetic conduc-
tivity of the masses disposed in proximity; that the
lines of magnetic force were strictly analogous to the
lines of electric flow in an electric circuit. He spoke of
a magnet surrounded by air being like unto a voltaic
battery immersed in water or other electrolyte. He
even saw the existence of a power, analogous to that of
electromotive force in electric circuits, though the name,
" magneto-motive force/' is of more recent origin. The
notion of magnetic conductivity is to be found in Max-
well's great treatise (vol. ii., p. 51), but is only briefly
mentioned. Rowland, 9 in 1873,- expressly adopted the
reasoning and language of Faraday's method in the work-
ing out of some new results on magnetic permeability,
and pointed out that the flow of magnetic lines of force

7 Ann. ofElectr., iv., 59, 1839; v., 195, 1841: and " Scientific Papers," pp. 8,
31, 35, 36.

8 " Experimental Researches, 11 vol. iii., art. 3117, 3228, 3230, 3260, 3271, 3276,
3294, and 3361.

Phil. Mag., series iv., vol. xlvi., Aug., 1873, ''On Magnetic Permeability
and the Maximum of Magnetism of Iron, Steel, and Nickel. 1 '

12 LECTURES ON THE ELECTROMAGNET

through a bar could be subjected to exact calculation;
the elementary law, he says, " is similar to the law of
Ohm." According to Rowland, the " magnetizing force
of helix " was to be divided by the " resistance to the
lines of force;" a calculation for magnetic circuits
which every electrician will recognize as precisely Ohm's
law for electric circuits. He applied- the calculations
to determine the permeability of certain specimens
of iron, steel, and nickel. In 1882, 10 and again in
1883, Mr. R. H. M. Bosanquet n brought out at greater
length a similar argument, employing the extremely apt
term " magneto-motive force " to connote the force tend-
ing to drive the magnetic lines of induction through the
" magnetic resistance," or, as it will frequently be called
in these lectures, the magnetic "reluctance/ 7 of the cir-
cuit. In these papers the calculations are reduced to a
system, and deal not only with the specific properties of
iron, but with problems arising out of the shape of the
iron. Bosanquet shows how to calculate the several re-
sistances (or reluctances) of the separate parts of the
circuit, and then add them together to obtain the total
resistance (or reluctance) of the magnetic circuit.

Prior to this, however, the principle of the magnetic
circuit had been seized upon by Lord Elphinstone and
Mr. Vincent, who proposed to apply it in the construc-
tion of dynamo-electric machines. On two occasions u

10 Proc. Roy. Soc., xxxiv., p. 445, Dec., 1882.

11 Phil Mag., series v., vol. xv., p. 205, Mar., 1883, "On Magneto-Motive
Force." Also ib., vol. xix., Feb., 1885, and Proc. Roy. Soc., No. 223, 1883.
See also The Electrician (London \ xiv., p. 291, Feb. 14, 1885.

12 Proc. Roy. Soc., xxix., p. 292, 1879, and xxx., p. 287, 1880. See Electrical
Review (London;, viii., p. 134, 1880.

LECTURES ON THE ELECTROMAGNET. 13

they communicated to the Royal Society the results of
experiments to show that the same exciting current
would evoke a larger amount of magnetism in a given
iron structure, if that iron structure formed a closed
magnetic circuit than if it were otherwise disposed.

In recent years the notion of the magnetic circuit has
been vigorously taken up by the designers of dynamo
machines,, who, indeed, base the calculation of their de-
signs upon this all-important principle. Having this,
they need no laws of inverse squares of distances, no
magnetic moments, none of the elaborate expressions for
surface distribution of magnetism, none of the ancient
paraphernalia of the last century. The simple law of
the magnetic circuit and a knowledge of the properties
of iron are practically all they need. About four years
ago, much was done by Mr. Gisbert Kapp 13 and by Drs.
J. and E. Hopkinson 14 in the application of these con-
siderations to the design of dynamo machines, which
previously had been a matter of empirical practice. To
this end the formulae of Professor Forbes 15 for calculat-
ing magnetic leakage, and the researches of Professors
Ayrton and Perry 16 on magnetic shunts, contributed .a
not unimportant share. As the result of the advances
made at that time, the subject of dynamo design was
reduced to an exact science.

It is the aim and object of the present course of lec-

13 The Electrician (London), vols. xiv., xv., and xvi., 1885-86; also Proc.
Inst. Civil Engineers, Ixxxiii., 1885-86; and Jour. Soc. Telegr. Engineers, xv.,
524, 1886.

14 Phil. Trans., 1886, pt. i., p. 331 ; and TJie Electrician (London), xviii., pp.
39, 63, 86, 1886.

15 Jour. Soc. Telegr. Engineers, xv., 555, 1886.

16 Jour. Soc. Telegr. Engineers, xv., 530, 1886.

14 LECTURES ON THE ELECTROMAGNET.

tnres to show how the same considerations which have
been applied with such great success to the subject of
the design of dynamo-electric machines may be applied
to the study of the electromagnet. The theory and
practice of the design and construction of electromag-
nets will thus be placed, once for all, upon a rational
basis. Definite rules will be laid down for the guidance
of the constructor, directing him as to the proper dimen-
sions and form of iron to be chosen, and as to the proper
size and amount of copper wire to be wound upon it in
order to produce any desired result.

First, however, a historical account of the invention
will be given, followed by a number of general consid-
erations respecting the uses and forms of electromag-
nets. These will be followed by a discussion of the mag-
netic properties of iron and steel and other materials;
some account being added of the methods used for de-
termining the magnetic permeability of various brands
of iron at different degrees of saturation. Tabular in-
formation is given as to the results found by different
observers. In connection with the magnetic properties
of iron, the phenomenon of magnetic hysteresis is also
described and discussed. The principle of the magnetic
circuit is then discussed with numerical examples, and
a number of experimental data respecting the perform-
ance of electromagnets are adduced, in particular those
bearing upon the tractive power of electromagnets. The
law of traction between an electromagnet and its arma-
ture is then laid down, followed by the rules for pre-
determining the iron cores and copper coils required to
give any prescribed tractive force.

LECTURES ON THE ELECTROMAGNET. 15

Then comes the extension of the calculation of the
magnetic circuit to those cases where there is an air-gap
between the poles of the magnet and the armature, and
where, in consequence, there is leakage of the magnetic
lines from pole to pole. The rules for calculating the
winding of the copper coils are stated, and the limiting
relation between the magnetizing power of the coil and
the heating effect of the current in it is explained. After
this comes a detailed discussion of the special varieties
of form that must be given to electromagnets in order
to adapt them to special services. Those which are
designed for maximum traction, for quickest action, for
longest range, for greatest economy when used in con-
tinuous daily service, for working in series with con-
stant current, for use in parallel at constant pressure,
and those for use with alternate currents are separately
considered.

Lastly, some account is given of the various forms of
electromagnetic mechanism which have arisen in con-
nection with the invention of the electromagnet. The
plunger and coil is specially considered as constituting
a species of electromagnet adapted for a long range of
motion. Modes of mechanically securing long range for
electromagnets and of equalizing their pull over the
range of motion of the armature are also described.
The analogies between sundry electro-mechanical move-
ments and the corresponding pieces of ordinary mech-
anism are traced out. The course is concluded by a
consideration of the various modes of preventing or
minimizing the sparks which occur in the circuits in
which electromagnets are used.

16 LECTURES ON THE ELECTROMAGNET.

HISTORICAL SKETCH.

The effect which an electric current, flowing in a wire,
can exercise upon a neighboring compass needle was dis-
covered by Oersted in 1820. 17 This first announcement
of the possession of magnetic properties by an electric cur-
rent was followed speedily by the researches of Ampere, 18
Arago. 19 Davy, 20 and by the devices of several other ex-
perimenters, including De La Rive's 21 floating battery
and coil; Schweigger's 22 multiplier, Cumming's 23 gal-
vanometer, Faraday's 24 apparatus for rotation of a per-
manent magnet, Marsh's 25 vibrating pendulum, and
Barlow's 26 rotating star-wheel. But it was not until
1825 that the electromagnet was invented, Davy had,
indeed, in 1821, surrounded with temporary coils of wire
the steel needles upon which he was experimenting, and
had shown that the flow of electricity around the coil
could confer magnetic power upon the steel needles.
But from this experiment it was a grand step forward
to the discovery that a core of soft iron, surrounded by
its own appropriate coil of copper, could be made to act
not only as a powerful magnet, but as a magnet whose
power could be turned on or off at will, could be aug-

17 See Thomson's Annals of Philosophy, Oct., 1820.
19 Ann. de Chim. et de Physique, xv., 59 and 170, 1820.

19 /&., xv., 93, 1820.

20 Phil. Trans., 1821.

21 "BibliothequeUniverselle," Mar., 1821.

i2 Ib. 23 camb. Phil. Trans., 1821.

24 Quarterly Journal of Science, Sept., 1821.

25 Barlow's " Magnetic Attractions," second edition, 1823.
^ Ib.

LECTURES ON THE ELECTROMAGNET. 17

men ted to any desired degree, and could be set into
action and controlled from a practically unlimited dis-
tance.

The electromagnet, in the form which can first claim
recognition for these qualities, was devised by William
Sturgeon, 27 and is described by him in the paper which
he contributed to the proceedings of the Society of Arts
in 1825, accompanying a set of improved apparatus for
electromagnetic experiments. 28 The Society of Arts
rewarded Sturgeon's labors by awarding him the silver
medal of the society and a premium of 30 guineas.
Among this set of apparatus are two electromagnets,

27 William Sturgeon, the inventor of the electromagnet, was born at Whit'
tingtou, in Lancasln're, in 1783. Apprenticed as a boy to the trade of a shoe-
maker, at the age of 19 he joined the Westmoreland militia, and two years
later enlisted into the Royal Artillery, thus gaining the chance of learning
something of science, and having leisure in which to pursue his absorbing
passion for chemical and physical experiments. He was 42 ye:irsof age
when he made his great, though at the time unrecognized, invention. At
the date of his researches in electromagnetism he was resident at 8 Artillery
place, Woolwich, at which place he was the associate of Marsh and was inti-
mate with Barlow, Christie, and Gregory, who interested themselves in his
work. In 1835 he presented a paper to the Royal Society containing descrip-
tions, inter alia, of a magneto-electric machine with longitudinally wound
armature, and with a commutator consisting of half discs of metal. For
some reason this paper was not admitted to the Philosophical Transactions;
he afterward printed it in full, without alteration, in his volume of ' Scien-
tific Researches, 11 published by subscription in 1850. From 1836 to 1H43 he
conducted the Annals of Electricity. He had now removed to Manchester,
where he lectured on electricity at the Royal Victoria Gallery. He died at
Prestwick, near Manchester, in 1850. There is a tablet to his menu >ry in the
church atKirkby Lonsdale, from which town the village of Whittington is dis-
tant about two miles. A portrait of Sturgeon in oils, and said to be an ex-
cellent likeness, is believed still to be in existence; but all inquiries as to its
whereabouts have proved unavailing. At the present moment, so far as I am
aware, the scientific world is absolutely without a portrait of the inventor of
the electromagnet.

8 Trans. Society of Arts, 1825, xliii., p. 38
2

18

LECTURES ON THE ELECTROMAGNET.

one of horseshoe shape (Figs. 1 and 2) and one a straight
bar (Fig. 3). It will be seen that the former figures
present an electromagnet consisting of a bent iron rod
about one foot long and a half inch in diameter, var-
nished over and then coiled with a single left-handed
spiral of stout uncovered copper wire of 18 turns. This

FIGS. 1 AND 2. STURGEON'S FIRST ELECTROMAGNET.

coil was found appropriate to the particular battery
which Sturgeon preferred, namely, a single cell contain-
ing a spirally enrolled pair of zinc and copper plates of
large area (about 130 square inches) immersed in acid;
which cell, having small internal resistance, would yield
a large quantity of current when connected to a circuit
of small resistance. The ends of the copper wire were
brought out sideways and bent down so as to dip in two

LECTURES ON THE ELECTROMAGNET.

deep connecting cups marked Z and (7, fixed upon a
wooden stand. These cups, which were of wood, served
as supports to hold up the electromagnet, and having
mercury in them served also to make good electrical
connection. In Fig. 2 the magnet is seen sideways,
supporting a bar of iron, y. The circuit was completed
to the battery through a connecting wire, d, which
could be lifted out of the
cup, Z, so breaking circuit
when desired, and allowing
the weight to drop. Stur-
geon added in his explana-
tory remarks that the poles,
N and 8, of the magnet will
be reversed if you wrap the
copper wire about the rod as
a right-handed screw, instead
of a left-handed one, or, more
simply, by reversing the con-
nections with the battery, by

Causing the wire that dips FIG. 3. STURGEON'S STRAIGHT-BAR
into the Z CUp to dip into the ELECTROMAGNET.

C cup, and vice versa. This electromagnet was capable
of supporting nine pounds when thus excited.

Fig. 3 shows another arrangement to fit on the same
stand. This arrangement communicates magnetism to
hardened steel bars as soon as they are put in, and ren-
ders soft iron within it magnetic during the time of
action; it only differs from Figs. 1 and 2 in being
straight, and thereby allows the steel or iron bars to slide
in and out.

20 LECTURES ON THE ELECTROMAGNET.

For this piece of apparatus and other adjuncts accom-
panying it, all of which are described in the Society's
Transactions for ]825, Sturgeon, as already stated,
was awarded the society's silver medal and a premium
of 30 guineas. The apparatus was deposited in the
museum of the society, which therefore might be sup-
posed to be the proud possessor of the first electromag-
net ever constructed. Alas ! for the vanity of human
affairs, the society's museum of apparatus has long been
dispersed, this priceless relic having been either made
over to the now defunct Patent-office Museum or other-
wise lost sight of.

Sturgeon's first electromagnet, the core of which
weighed about seven ounces, was able to sustain a load
of nine pounds, or about 20 times its own weight. At
the time it was considered a truly remarkable perform-
ance. Its single layer of stout copper wire was well
adapted to the battery employed, a single cell of Stur-
geon's own particular construction having a surface of
130 square inches, and therefore of small internal resist-
ance. Subsequently, in the hands of Joule, the same
electromagnet sustained a load of 50 pounds, or about
114 times its own weight. Writing in 1832 about his
apparatus of 1825, Sturgeon used the following magnil-
oquent language :

"When first I showed that the magnetic energies of a
galvanic conducting wire are more conspicuously exhibited
by exercising them on soft iron than on hard steel, my ex
pertinents were limited to small masses generally to a few
inches of rod iron about half an inch in diameter. Some of
those pieces were employed while straight, and others were

LECTURES ON THE ELECTROMAGNET. 21

bent into the form of a horseshoe magnet, each piece being
compassed by a spiral conductor of copper wire. The mag-
netic energies developed by these simple arrangements are
of a very distinguished and exalted character, as is conspic-
uously manifested by the suspension of a considerable
weight at the poles during the period of excitation by the
electric influence.

"An unparalleled transiliency of magnetic action is also
displayed in soft iron by an instantaneous transition from
a state of total inactivity to that of vigorous polarity, and
also by a simultaneous reciprocity of polarity in the ex-
tremities of the bar versatilities in this branch of physics
for the display of which soft iron is pre-eminently qualified,
and which, by the agency of electricity, become demonstra-
ble with the celerity of thought, and illustrated by experi-
ments the most splendid in magnetics. It is, moreover,
abundantly manifested by ample experiments, that gal-
vanic electricity exercises a superlative degree of excitation
on the latent magnetism of soft iron, and calls for its recon-
dite powers with astonishing promptitude, to an intensity
of action far surpassing anything which can be accom-
plished by any known application of the most vigorous per-
manent magnet, or by any other mode of experimenting
hitherto discovered. It has been observed, however, by
experimenting on different pieces selected from various
sources, that, notwithstanding the greatest care be observed
in preparing them of a uniform figure and dimensions, there
appears a considerable difference in the susceptibility which
they individually possess of developing the magnet powers,
much of which depends upon the manner of treatment at
the forge, as well as upon the natural character of the iron
itself. 29

29 " I have made a number of experiments on small pieces, from the re-
sults of which it appears that much hammering is highly detrimental to the
development of magnetism in soft iron, whether the exciting cause be gal-
vanic or any other. And although good annealing is always essential and
facilitates to a considerable extent the display of polarity, that process is

22 LECTURES ON THE ELECTROMAGNET.

"The superlative intensity of electromagnets, and the
facility and promptitude with which their energies can be
brought into play, are qualifications admirably adapted for
their introduction into a variety of arrangements in which
powerful magnets so essentially operate and perform a dis-
tinguished part in the production of electromagnetic rota-
tions ; while the versatilities of polarity of which they are
susceptible are eminently calculated to give a pleasing di-
versity in the exhibition of that highly interesting class of
phenomena, and lead to the production of others inimita-
ble by any other means." 30

Sturgeon's further work during the next three years
is best described in his own words :

" It does not appear that any very extensive experiments
were attempted to improve the lifting power of electromag-
nets, from the time that my experiments were published in
the Transactions of the Society of Arts, etc., for 1825, till
the latter part of 1828. Mr. Watkins, philosophical instru-
ment maker, Charing Cross, had, however, made them of
much larger size than any which I had employed, but I am
not aware to what extent he pursued the experiment.

" In the year 1828, Professor Moll, of Utrecht, being on a
visit to London, purchased of Mr. Watkins an electromag-
net weighing about five pounds at that time, I believe, the
largest which had been made. It was of round iron, about
one inch in diameter, and furnished with a single copper
wire twisted round it 83 times. When this magnet was ex-
cited by a large galvanic surface, it supported about 75
pounds. Professor Moll afterward prepared another electro-
very far from restoring to the iron that degree of susceptibility which it fre-
quently loses by the operation of the hammer. Cylindric rod iron of small
dimensions may very easily be bent into the required form, without any ham-
mering whatever; and I have found that small electromagnets made in this
way display the magnetic powers in a very exalted degree/'

30 Sturgeon's " Scientific Researches," p. 113.

LECTURES ON THE ELECTROMAGNET 23

magnet, which, when bent, was 12-J inches high, 2i inches
in diameter, and weighed about 26 pounds, prepared, like
the former, with a single spiral conducting wire. With an
acting galvanic surface of 11 square feet, this magnet would
support 154 pounds, but would not lift an anvil which
weighed 200 pounds.

" The largest electromagnet which I have yet [1832] ex-
hibited in my lectures weighs about 16 pounds. It is formed
of a small bar of soft iron, 1| inches across each side ; the
cross-piece which joins the poles is from the same rod of
iron, arid about 3f inches long. Twenty separate strands
of copper wire, each strand about 50 feet in length, are
coiled around the iron, one above another, from pole to
pole, and separated from each other by intervening cases
of silk ; the first coil is only the thickness of one ply of silk
from the iron; the twentieth, or outermost, about half an
inch from it. By this means the wires are completely in-
sulated from each other without the trouble of covering
them with thread or varnish. The ends of wire project
about two feet for the convenience of connection. With
one of my small cylindrical batteries, exposing about 150
square inches of total surface, this electromagnet supports
400 pounds. I have tried it with a larger battery, but its
energies do not seem to be so materially exalted as might
have been expected by increasing the extent of galvanic
surface. Much depends upon a proper acid solution ; good
nitric or nitrous acid, with about six or eight times its quan-
tity of water, answers very well. With a new battery of
the above dimensions and a strong solution of salt and
water, at a temperature of 190 degrees Fahr., the electro-
magnet supported between 70 and 80 pounds when the first
17 coils only were in the circuit. With the three exterior
coils alone in the circuit, it would just support the lifter or
cross-piece. When the temperature of the solution was be-
tween 40 and 50 degrees, the magnetic force excited was
comparatively very feeble. With the innermost coil alone

24 LECTURES ON THE ELECTROMAGNET.

and a strong acid solution this electromagnet supports
about 100 pounds ; with the four outermost wires about 250
pounds. It improves in power with every additional coil
until about the twelfth, but not perceptibly any further;
therefore the remaining eight coils appear to be useless,
although the last three, independently of the innermost 17,
and at the distance of half an inch from the iron, produce
in it a lifting power of 75 pounds.

" Mr. Marsh has fitted up a bar of iron much larger than
mine with a similar distribution of the conducting wires to
that devised and so successfully employed by Professor
Henry. Mr. Marslfs electromagnet will support about 560
pounds when excited by a galvanic battery similar to mine.
These two, I believe, are the most powerful electromagnets
yet produced in this country.

"A small electromagnet, which I also employ on the lec-
ture table, and the manner of its suspension, is represented
by Fig. 3, Plate VI. The magnet is of cylindric rod iron
and weighs four ounces ; its poles are about a quarter of an
inch asunder. It is furnished with six coils of wire in the
same manner as the large electromagnet before described,
and will support upward of 50 pounds.

" I find a triangular gin very convenient for the suspen-
sion of the magnet in these experiments. A stage of thin
board, supporting two wooden dishes, is fastened, at a
proper height, to two of the legs of the gin. Mercury is
placed in these vessels, and the dependent amalgamated
extremities of the conducting wires dip into it one into
each portion.

" The vessels are sufficiently wide to admit of considerable
motion of the wires in the mercury without interrupting
the contact, which is sometimes occasioned by the swinging
Of the magnet and attached weight. The circuit is com-
pleted by other wires, which connect the battery with these
two portions of mercury. When the weight is supported
as in the figure, if an interruption be made by removing

LECTURES ON THE ELECTROMAGNET. 25

either of the connecting wires, the weight instantaneously
drops on the table. The large magnet I suspend in the
same way on a larger gin ; the weights which it supports
are placed one after another on a square board, suspended
by means of a cord at each corner from a hook in the cross-
piece, which joins the poles of the magnet.
" With a new battery and a solution of salt and water, at

FIG. 4. STURGEON'S LECTURE-TABLE ELECTROMAGNET.

a temperature of 190 degrees Fahr., the small electromag-
net, Fig. 3, Plate VI., supports 10 pounds." (See Fig. 4.)

In 1840, after Sturgeon had removed to Manchester,
where he assumed the management of the " Victoria
Gallery of Practical Science," he continued his work,
and in the seventh memoir in his series of researches he
wrote as follows :

26 LECTURES ON THE ELECTROMAGNET.

" The electromagnet belonging to this institution is made
of a cylindrical bar of soft iron, bent into the form of a
horseshoe magnet, having the two branches parallel to each
other arid at the distance of 4.5 inches. The diameter of the
iron is 2.75 inches; it is 18 inches long when bent. It is sur-
rounded by 14 coils of copper wire, seven on each branch.
The wire which constitutes the coils is one-twelfth of an
inch in diameter, and in each coil there are about 70 feet
of wire. They are united in the usual way with branch
wires, for the purpose of conducting the currents from the
battery. The magnet was made by Mr. Nesbit. . . . The
greatest weight sustained by the magnet in these experi-
ments is 12f hundred-weight, or 1,386 pounds, which was
accomplished by 16 pairs of plates, in four groups of four
pairs in series each. The lifting power by 19 pairs in series
was considerably less than by 10 pairs in series ; and but
very little greater than that given by one cell or one pair
only. This is somewhat remarkable, and shows how easily
we may be led to waste the magnetic powers of batteries by
an injudicious arrangement of its elements." 31

At the date of Sturgeon's work the laws governing
the flow of electric currents in wires were still obscure.
Ohm's epoch-making enunciation of the law of the elec-
tric circuit appeared in Poggendorff's Annalen in the
very year of Sturgeon's discovery, 1825, though his
complete book appeared only in 1827, and his work,,
translated by Dr. Francis into English, only appeared
(in Taylors "Scientific Memoirs/' vol. ii.) in 1841.
Without the guidance of Ohm's law it was not strange
that even the most able experimenters should not un-
derstand the relations between battery and circuit which
would give them the best effects. These had to be

31 Sturgeon's "Scientific Researches," p. 188.

LECTURES ON THE ELECTROMAGNET. 7

found by the painful method of trial and failure. Pre*-
eminent among those who tried was Prof. Joseph Henry,
then of the Albany Institute in New York, later of
Princeton, N. J., who succeeded in effecting an impor-
tant improvement. In 1828, led on by a study of the
" multiplier " (or galvanometer), he proposed to apply
to electromagnetic apparatus the device of winding
them with a spiral coil of wire " closely turned on it-
self/' the wire being of copper from one-fortieth to one-
twenty-fifth of an inch in diameter, covered with silk.
In 1831 he thus describes 32 the results of his experi-
ments :

"A round piece of iron, about one-quarter of an inch in
diameter, was bent into the usual form of a horseshoe, and
instead of loosely coiling around it a few feet of wire, as is
usually described, it was tightly wound with 35 feet of wire
covered with silk, so as to form about 400 turns; a pair of
small galvanic plates, which could be dipped into a tumbler
of diluted acid, was soldered to the ends of the wire and
the whole mounted on a stand. With these small plates
the horseshoe became much more powerfully magnetic than
another of the same size, and wound in the same manner,
by the application of a battery composed of 28 plates of
copper and zinc, each eight inches square. Another con-
venient form of this apparatus was contrived by winding
a straight bar of iron nine inches long with 35 feet of wire
and supporting it horizontally on a small cup of copper
containing a cylinder of zinc ; when this cup, which served
the double purpose of a stand and the galvanic element,
was filled with dilute acid the bar became a portable elec-
tromagnet. These articles were exhibited to the institute
in March, 1829. The idea afterward occurred to me that r,

sa SillimarTs American Journal of Science, Jan., 1831, xix., p. 400.

28 LECTURES ON THE ELECTROMAGNET.

sufficient quantity of galvanism was furnished by the two
small plates to develop, by means of the coil, a much greater
magnetic power in a larger piece of iron. To test this, a
cylindrical bar of iron, half an inch in diameter and about
10 inches long, was bent into the shape of a horseshoe, ahd
wound with 80 feet of wire ; with a pair of plates containing
only 2| square inches of zinc it lifted 15 pounds avoirdupois.
At the same time a very material improvement in the for-
mation of the coil suggested itself to me on reading a more
detailed account of Professor Schweigger's galvanometer,
and which was also tested with complete success upon the
same horseshoe; it consisted in using several strands of
wire, each covered with silk, instead of one. Agreeably to
this construction a second wire, of the same length as the
first, was wound over it, and the ends soldered to the zinc
and copper in such a manner that the galvanic current
might circulate in the same direction in both, or in other
words that the two wires might act as one ; the effect by
this addition was doubled, as the horseshoe, with the same
plates before used, now supported 28 pounds.

" With a pair of plates four inches by six inches it lifted
39 pounds, or more than 50 times its own weight.

" These experiments conclusively proved that a great de-
velopment of magnetism could be effected by a very small
galvanic element, and also that the power of the coil Avas
materially increased by multiplying the number of wires
without increasing the number of each. 11 33

Not content with these results, Professor Henry
pushed forward on the line he had thus struck out. He
was keenly desirous to ascertain how large a magnetic
force lie could produce when using only currents of
such a degree of smallness as could be transmitted
through the comparatively thin copper wires, such as

" "Scientific Writings of Joseph Henry, 11 p. 39.

LECTURES ON THE ELECTROMAGNET. 29

bell-hangers use. During the year 1830 he made great
progress in this direction, as the following extracts show :

" In order to determine to what extent the coil could be
applied in developing magnetism in soft iron, and also to
ascertain, if possible, the most proper length of the wires to
be used, a series of experiments was instituted jointly by
Dr. Philip Ten Eyck and myself. For this purpose 1,060
feet (a little more than one-fifth of a mile) of copper wire
of the kind called bell wire, .045 of an inch in diameter,
were stretched several times across the large room of the
Academy.

" Experiment 1. A galvanic current from a single pair of
plates of copper and zinc two inches square was passed
through the whole length of the wire, and the effect on a
galvanometer noted. From the mean of several observa-
tions, the deflection of the needle was 15 degrees.

" Experiment 2. A current from the same plates was
passed through half the above length, or 530 feet of wire ;
the deflection in this instance was 21 degrees.

" By a reference to a trigonometrical table, it will be seen
that the natural tangents of 15 degrees and 21 degrees are
very nearly in the ratio of the square roots of 1 and 2, or of
the relative lengths of the wires in these two experiments.

" The length of the wire forming the galvanometer may
be neglected, as it was only 8 feet long.

" Experiment 3. The galvanometer was now removed,
and the whole length of the wire attached to the ends of
the wire of a small soft iron horseshoe, a quarter of an inch
iri diameter, and wound with about eight feet of copper
wire with a galvanic current from the plates used in expe-
riments 1 and 2. The magnetism was scarcely observable
in the horseshoe.

"Experiment 4. The small plates were removed and a
battery composed of a piece of zinc plate four inches by
seven inches, surrounded with copper, was substituted.

30 LECTURES ON THE ELECTROMAGNET.

When this was attached immediately to the ends of the
eight feet of wire wound round the horseshoe, the weight
lifted was 4i pounds ; when the current was passed through
the whole length of wire (1,060 feet) it lifted about half an
ounce.

" Experiment 5. The current was passed through half
the length of wire (530 feet) with the same battery ; it then
lifted two ounces.

" Experiment 6. Two wires of the same length as in the
last experiment were used, so as to form two strands from
the zinc and copper of the battery ; in this case the weight
lifted was four ounces.

" Experiment 7. The whole length of the wire was at-
tached to a small trough on Mr. Cruickshanks' plan, con-
taining 25 double plates, and presenting exactly the same
extent of zinc surface to the action of the acid as the battery
used in the last experiment. The weight lifted in this case
was eight ounces ; when the intervening wire was removed
and the trough attached directly to the ends of the wire
surrounding the horseshoe, it lifted only seven ounces. . . .

" It is possible that the different states of the trough with
respect to dryness may have exerted some influence on this
remarkable result ; but that the effect of a current from a
trough, if not increased, is but slightly diminished in pass-
ing through a long wire is certain. . . .

" But be this as it may, the fact that the magnetic action
of a current from a trough is, at least, not sensibly dimin-
ished by passing through a long wire is directly applicable
to Mr. Barlow's project of forming an electromagnetic tele-
graph ; and it is also of material consequence in the con-
struction of the galvanic coil. From these experiments it is
evident that in forming the coil we may either use one very
long wire or several shorter ones, as the circumstances may
require ; in the first case, our galvanic combinations must
consist of a number of plates, so as to give ' projectile force ; '
in the second it must be formed of a single pair.

LECTURES ON THE ELECTROMAGNET. 31

" In order to test on a large scale the truth of these pre-
liminary results, a bar of soft iron, two inches square and
20 inches long, was bent into the form of a horseshoe 9|
inches high. The sharp edges of the bar were first a little
rounded by the hammer it weighed 21 pounds; a piece of
iron from the same bar, weighing seven pounds, was filed
perfectly flat on one surface, for an armature or lifter ; the
extremities of the legs of the horseshoe were also truly
ground to the surface of the armature ; around this horse-
shoe 540 feet of copper bell wire were wound in nine coils of
60 feet each; these coils were not continued around the
whole length of the bar, but each strand of wire, according
to the principle before mentioned, occupied about two
inches, and was coiled several times backward and forward
over itself; the several ends of the wires were left project-
ing and all numbered, so that the first and last end of each
strand might be readily distinguished. In this manner we
formed an experimental magnet on a large scale, with which
several combinations of wire could be made by merely unit-
ing the different projecting ends. Thus if the second end
of the first wire be soldered to the first end of the second
wire, and so on through all the series, the whole will form
a continuous coil of one long wire.

"By soldering different ends the whole may be formed in
a double coil of half the length, or into a triple coil of one-
third the length, etc. The horseshoe was suspended in a
strong rectangular wooden frame, 3 feet 9 inches high and
20 inches wide; an iron bar was fixed below the magnet, so
as to act as a lever of the second order ; the different weights
supported were estimated by a sliding weight in the same
manner as with a common steel-yard (see sketch). In the
experiments immediately following (all weights being avoir-
dupois) a small single battery was used, consisting of two
concentric copper cylinders with zinc between them; the
whol amount of zinc surface exposed to the acid from
both sides of the zinc was two-fifths of a square foot; the

32 LECTURES ON THE ELECTROMAGNET.

battery required only half a pint of dilute acid for its sub-
mersion.

" Experiment 8. Each wire of the horseshoe \ soldered
to the battery in succession, one at a time ; the agnetism
developed by each was just sufficient to support the weight
of the armature, weighing seven pounds.

" Experiment 9. Two wires, one on each side of the arch
of the horseshoe, were attached ; the weight lifted was 145
pounds.

" Experiment 10. With two wires, one from each extrem-
ity of the legs, the weight lifted was 200 pound

" Experiment 11. With three wires, one from each ex-
tremity of the legs and one from the middle of the arch,
the weight supported was 300 pounds.

" Experiment 12. With four wires, two from each ex-
tremity, the weight lifted was 500 pounds and the armature ;
when the acid was removed from the zinc, the magnet con-
tinued to support for a few minutes 130 pounds.

" Experiment 13. With six wires the weight supported
was 570 pounds; in all these experiments the wires were
soldered to the galvanic element ; the connection in no case
was formed with mercury.

"Experiment^. When all the wires (nine in number)
were attached, the maximum weight lifted was 650 pounds,
and this astonishing result, it must be remembered, was
produced by a battery containing only two-fifths of a square
foot of zinc surface, and requiring only half a pint of dilute
acid for its submersion.

" Experiment 15. A small battery, formed with a plate
of zinc 12 inches long and 6 inches wide, and surrounded by
copper, was substituted for the galvanic elements used in the
last experiment ; the weight lifted in this case was 750 pounds.

" Experiment 16. In order to ascertain the effect of a
very small galvanic elem'ent on this large quantity of iron,
a pair of plates exactly one inch square was attached to all
the wires ; the weight lifted was 85 pounds.

LECTURES ON THE ELECTROMAGNET. 33

" The following experiments were made with wires of dif-
ferent lengths on the same horseshoe :

" Experiment 17. With six wires, each 30 feet long, at-
tached to the galvanic element, the weight lifted was 875
pounds.

" Experiment 18. The same wires used in the last experi-
ment were united so as to form three coils of GO feet each;
the weight supported was 290 pounds. This result agrees
nearly with that of experiment 11, though the same indi-
vidual wires were not used; from this it appears that six
short wires are more powerful than three of double the
length.

' Experiment 19. The wires used in experiment 10, but
united so as to form a single noil of 120 feet of wire, lifted 00
pounds; while in experiment 10 the weight lifted was 200
pounds. This is a confirmation of the result in the last ex-
periment. . . .

" In these experiments a fact was observed which appears
somewhat surprising : when the large battery was attached,
and the armature touching both poles of the magnet, it
was capable of supporting more than 700 pounds, but when
only one pole was in contact it did riot support more than
five or six pounds, and in this case we never succeeded in
making it lift the armature (weighing seven pounds). This
fact may perhaps be common to all large magnets, but we
have never seen the circumstance noticed of so great a dif-
ference between a single pole and both. . . .

"A series of experiments was separately instituted by Dr.
Ten Eyck, in order to determine the maximum development
of magnetism in a small quantity of soft iron.

" Most of the results given in this paper were witnessed
by Dr. L. C. Beck, and to this gentleman we are indebted
for several suggestions, and particularly that of substitut-
ing cotton well waxed for silk thread, which in these in-
vestigations became a very considerable item of expense.
He also made a number of experiments with iron bonnet

34 LECTURES ON THE ELECTROMAGNET.

wires, which, being found in commerce already wound,
might possibly be substituted in place of copper. The re-
sult was that with very short wire the effect was nearly the
same as with copper, but in coils of long wire with a small
galvanic element it was not found to answer. Dr. Beck
also constructed a horseshoe of round iron one inch in
diameter, with four coils on the plan before described.
With one wire it lifted 30 pounds, with two wires 60 pounds,
with three wires 85 pounds, and with four wires 112 pounds.
While we were engaged in these investigations, the last
number of the Edinburgh Journal of Science was received
containing Professor Moll's paper on ' Electromagnetism.'
Some of his results are in a degree similar to those here de-
scribed ; his object, however, was different, it being only to
induce strong magnetism on soft iron with a powerful gal-
vanic battery. The principal object in these experiments
was to produce the greatest magnetic force with the small-
est quantity of galvanism. The only effect Professor Moll's
paper has had over these investigations has been to hasten
their publication; the principle on which they were insti-
tuted was known to us nearly two years since, and at that
time exhibited to the Albany Institute." 34

In the next number of Silliman's Journal (April,
1831) Professor Henry gave " an account of a large elec-
tromagnet made for the laboratory of Yale College."
The core of the armature weighed 59^ pounds; it was
forged under Henry's own direction,, and wound "by Dr.
Ten Eyck. This magnet, wound with 26 strands of
copper bell wire of a total length of 728 feet, and excited
by two cells which exposed nearly 4J square feet of sur-
face, readily supported on its armature, which weighed
23 pounds, a load of 2,063 pounds.

34 " Scientific Writings of Joseph Henry, 11 p. 49.

LECTURES ON THE ELECTROMAGNET. 35

Writing in 1867 of his earlier experiments, Henry

FIG. 5. HENRY'S ELECTROMAGNET. 35

35 This figure, copied from the Scientific American, Dec. 11, 1880, represents
Henry's electromagnet still preserved in Princeton College. The other appa-
ratus at the foot, including a current-reverser, and the ribbon-coil used in the
famous experiments on secondary and tertiary currents, were mostly con-
structed by Henry's own hands.

36 LECTURES ON THE ELECTROMAGNET.

speaks 36 thus of his ideas respecting the use of addi-
tional coils on the magnet and the increase of battery
power:

" To test these principles on a larger scale the experimen-
tal magnet was constructed, which is shown in Fig. 6. In
this a number of compound helices were placed on the same
bar, their ends left projecting, and so numbered that they
could all be united into one long helix,
OT variously combined in sets of lesser
length.

" From a series of experiments with
this and other magnets, it was proved
that in order to produce the greatest
amount of magnetism from a battery
of a single cup a number of helices is
required ; but when a compound bat-
FIG. 6. HENRY'S Ex- tery is used then one long wire must
ELECTRO " be employed, making many turns
around the iron, the length of wire,
and consequently the number of turns, being commensu-
rate with the projectile power of the battery.

" In describing the results of rny experiments, the terms
'intensity' and .' quantity ' magnets were introduced to
avoid circumlocution, and were intended to be used merely
in a technical sense. By the intensity magnet I designated
a piece of soft iron, so surrounded with wire that its mag-
netic power could be called into operation by an intensity
battery ; and by a quantity magnet, a piece of iron so sur-
rounded by a number of separate coils that its magnetism
could be fully developed by a quantity battery.

" I was the first to point out this connection of the two
kinds of the battery with the two forms of the magnet, in

36 Statement in relation to the history of the electromagnetic telegraph,
from the Smithsonian Annual Report for 1857, p. 99.

LECTURES ON THE ELECTROMAGNET. 37

my paper, in Si Hi marts Journal, January, 1831, and clearly
to state that when magnetism was to be developed by
means of a compound battery one long coil must be em-
ployed, and when the maximum effect was to be produced
by a single battery a number of single strands should be
used. . . . Neither the electromagnet of Sturgeon nor any
electromagnet ever made previous to my investigations
was applicable to transmitting power to a distance. . . .
The electromagnet made by Sturgeon and copied by Dana,
of New York, was an imperfect quantity magnet, the feeble
power of which was developed by a single battery. 1 '

Finally, Henry 37 sums up his own position as fol-
lows :

" 1. Previous to my investigations the means of develop-
ing magnetism in soft iron were imperfectly understood,
and the electromagnet which then existed was inapplicable
to transmissions of power to a distance.

" 2. I was the first to prove by actual experiment that in
order to develop magnetic power at a distance a galvanic
battery of ' intensity' must be employed to project the cur-
rent through the long conductor, and that a magnet sur-
rounded by many turns of one long wire must be used to
receive this current.

" 3. I was the first to actually magnetize a piece of iron at
a distance, and to call attention to the fact of the applica-
bility of my experiments to the telegraph.

" 4. I was the first to actually sound a bell at a distance
by means of the electromagnet.

"5. The principles I had developed were applied by Dr.
Grale to render Morse's machine effective at a distance."

Though Henry's researches were published in 1831,

s ' " Scientific Writings of Joseph Henry," vol. ii., p. 435.

38 LECTURES ON THE ELECTROMAGNET.

they were for some years almost unknown in Europe.
Until April, 1837, when Henry himself visited Wheat-
stone at his laboratory at King's College, the latter did
not know how to construct an electromagnet that could
be worked through a long wire circuit. Cooke, who
became the coadjutor of Wheatstone, had originally
come to him to consult him, 38 in February, 1837, about
his telegraph and alarum, the electromagnets of which,
though they worked well on short circuits, refused to
work when placed in circuit with even a single mile of
wire. Wheats tone's own account 39 of the matter is
extremely explicit : " Relying on my former experience,
I at once told Mr. Cooke that his plan would not and
could not act as a telegraph, because sufficient attractive
power could not be imparted to an electromagnet inter-
posed in a long circuit; and, to convince him of the
truth of this assertion, I invited him to King's College
to see the repetition of the experiments on which my
conclusion was founded. He came, and after seeing a
variety of voltaic magnets, which even with powerful
batteries exhibited only slight adhesive traction, he
expressed his disappointment."

After Henry's visit to Wheatstone, the latter altered
his tone. He had been using, faute de mieux, relay cir-
cuits to work the electromagnets of his alarum in a
short circuit with a local battery. "These short cir-
cuits," he writes, "have lost nearly all their importance

38 See Mr. Latimer Clark's account of Cooke in vol. viii. of Jour. Soc.
Telegr. Engineers, p. 374. 1880.

39 W. F. Cooke, "The Electric Telegraph ; Was it Invented by Prof. Wheat-
stone?" 1856-57, part ii., p. 87.

LECTURES ON THE ELECTROMAGNET. 30

and are scarcely worth contending about since my dis-
covery " (the italics are our own) " that electromagnets
may be so constructed as to produce the required effects
by means of the direct current, even in very long cir-
cuits." 40

We pass on to the researches of the distinguished
physicist of Manchester, whose decease we have lately
had to deplore, Mr. James Prescott Joule, who, fired by
the work of Sturgeon, made most valuable contributions
to the subject. Most of these were published either in
Sturgeon's Annals of Electricity, or in the Proceedings
of the Literary and Philosophical Society of Manchester,
but their most accessible form is the republished vol-
ume issued five years ago by the Physical Society of
London.

In his earliest investigations he was endeavoring to
work out the details of an electric motor. The follow-
ing is an extract from his own account (" Reprint of
Scientific Papers," p. 7) :

" In the further prosecution of my inquiries, I took six
pieces of round bar iron of different diameters and lengths,
also a hollow cylinder, one -thirteenth of an inch thick in
the metal. These were bent in the U-form, so that the
shortest distance between the poles of each was half an
inch ; each was then wound with 10 feet of covered copper
wire, one-fortieth of an inch in diameter. Their attractive
powers under like currents for a straight steel magnet, 1
inches long, suspended horizontally to the beam of a bal-
ance, were, at the distance of half an inch, as follows : (See
table on page 40. )

"A steel magnet gave an attractive power of 23 grains,
while its lifting power was not greater than 00 ounces.

Ib., p. 95.

40

LECTURES ON THE ELECTROMAGNET.

^>

o

*3

"3

gi

a

O-Q
fe

r-2
0-3
k;d2

:^
1

^2

S3

"is

K0

!^32

2^

8

3.6

28

Length round the bend in
inches. .
Diameter in inches
Attraction for steel magnet, in
grains
Weight lifted, in ounces

6

M

7.5
36

5^

6.3
52

5.1

92

5.0
36

1

4.1
52

a

4.8

20

" The above results will not appear surprising if we
consider, first, the resistance which iron presents to the
induction of magnetism, and, second, how very much the
induction is exalted by the completion of the magnetic
circuit.

" Nothing can be more striking than the difference be-
tween the ratios of lifting to attractive power at a distance
in the different magnets. While the steel magnet attracts
with a force of 23 grains and lifts 60 ounces, the electromag-
net No. 3 attracts with a force of only 5.1 grains, but lifts
as much as 92 ounces.

" To make a good electromagnet for lifting purposes . 1st.
Its iron, if of considerable bulk, should be compound, of
good quality, and well annealed. 3d. The bulk of the iron
should bear a much greater ratio to its length than is gen-
erally the case. 3d. The poles should be ground quite true,
arid fit flatly and accurately to the armature. 4th. The
armature should be equal in thicknesi to the iron of the
magnet.

" In studying what form of electromagnet is best for at-
traction from a distance, two things must be considered,
viz., the length of the iron and its sectional area.

" Now I have always found it disadvantageous to increase
the length beyond what is needful for the winding of the
covered wire. 1 '

These results were announced in March, 1839. In
May of the same year he propounded a law of the mutual

LECTURES ON THE ELECTROMAGNET. 41

attraction of two electromagnets as follows: "The at-
tractive force of two electromagnets for one another is
directly proportional to the square of the electric force
to which the iron is exposed; or if j? denote the elec-
tric current, TFthe length of wire, and M the magnetic
attraction, M=E*W*" The discrepancies which he
himself observed he rightly attributed to the iron be-
coming saturated magnetically. In March, 1840, he ex-

FIG. 7. JOULE'S ELECTROMAGNET.

tended this same law to the lifting power of the horse-
shoe electromagnet.

In August, 1840, he wrote to i\\Q Annals of Electricity
on electromagnetic forces, dealing chiefly with some
special electromagnets for traction. One of these pos-
sessed the form shown in Fig. 7. Both the magnet and
the iron keeper were furnished with eye-holes for the
purpose of suspension and measurement of the force
requisite to detach the keeper. Joule thus writes about
the experiments : 41

" I proceed now to describe my electromagnets, which I
constructed of very different sizes in order to develop any

41 " Scientific Papers, 11 vol. i., p. 30.

42 LECTURES ON THE ELECTROMAGNET.

curious circumstance which might present itself. A piece
of cylindrical wrought iron, eight inches long, had a hole
one inch in diameter bored the whole length of its axis,
one side was planed until the hole was exposed sufficiently
to separate the thus formed poles one-third of an inch.
Another piece of iron, also eight inches long, was then
planed, and, being secured with its face in contact with the
other planed surface, the whole was turned into a cylinder
eight inches long, 3f inches in exterior, and one inch interior
diameter. The larger piece was then covered with calico
and wound with four copper wires covered with silk, each
23 feet long and one-eleventh of an inch in diameter a
quantity just sufficient to hide the exterior surface, and to
fill the interior opened hole. . . . The above is designated
No. 1 ; and the rest are numbered in tha order of their de-
scription.

" I made No. 2 of a bar of half- inch round iron 2. 7 inches
long. It was bent into an almost semicircular shape and
then covered with seven feet of insulated copper wire ^ inch
thick. The poles are half an inch asunder, and the wire
completely fills the space between them.

"A third electromagnet was made of a piece of iron 0. 7
inch long, 0.37 inch broad, and 0.15 inch thick. Its edges
were reduced to such an extent that the transverse section
was elliptical. It was bent into a semicircular shape, and
wound with 19 inches of silked copper wire fa inch in diam-
eter.

" To procure a still more extensive variety, I constructed
what might, from its extreme minuteness, be termed an ele-
mentary electromagnet. It is the smallest, I believe, ever
made, consisting of a bit of iron wire \ inch long and fa inch
in diameter. It was bent into the shape of a semicircle,
and was wound with three turns of uninsulated copper wire
fa inch in thickness."

With these magnets experiments were made with vari-

LECTURES ON THE ELECTROMAGNET. 43

ous strengths of currents, the tractive forces being
measured by an arrangement of levers. The results,
briefly, are as follows : Electromagnet No. 1, the iron
of which weighed ] 5 pounds, required a weight of 2,090
pounds to detach the keeper. No. 2, the iron of which
weighed 1,057 grains, required 49 pounds to detach its
armature. No. 8, the iron of which weighed 65.3 grains,
supported a load of 12 pounds, or 1,280 times its own
weight. No. 4, the weight of which was only half a
grain, carried in one instance 1,41 7 grains, or 2,834 times
its own weight.

" It required much patience to work with an arrangement
so minute as this last ; and it is probable that I might ulti-
mately have obtained a larger figure than the above, which,
however, exhibits a power proportioned to its weight far
greater than any on record, and is eleven times that of the
celebrated steel magnet which belonged to Sir Isaac New-
ton.

" It is well known that a steel magnet ought to have a
much greater length than breadth or thickness; and Mr.
Scoresby has found that when a large number of straight
steel magnets are bundled together, the power of each when
separated and examined is greatly deteriorated. All this is
easily understood, and finds its cause in the attempt of each
part of the system to induce upon the other part a contrary
magnetism to its own. Still there is no reason why the
principle should in all cases be extended from the steel to
-the electromagnet, since in the latter case a great and com-
manding inductive power is brought into play to sustain
what the former has to support by its own unassisted re-
tentive property. All the preceding experiments support
this position; and the following table gives proof of the
obvious and necessary general consequence: the maximum
power of the electromagnet is directly proportional to its

44

LECTURES ON THE ELECTROMAGNET.

least transverse sectional area. The second column of the
table contains the least sectional area in square inches of
the entire magnetic circuit. The maximum power in pounds
avoirdupois is recorded in the third; and this, reduced to
an inch square of sectional area, is given in the fourth col-
umn under the title of specific power.

TABLE I.

DESCRIPTION.

ip

Maximum
power.

If

f Xo. 1
My own electromagnets ' ^' | ' '

[NO! '4. '.'.'.'..'..'..'.'".'.'.'.'.

Mr. J. C. Nesbit's.- Length round the curve, 3
feet ; diameterof iron core, 2% inches : sectional
area, 5.7 inches; do. of armature, 4.5 inches;
\\ eight of iron, about 50 pounds

10
0.196
0.0436
0.0012

4 5

2,090
49
12
0.202

1 48

900

250

275
1C2

317

Prof. Henry's. Lengi h round the curve. 20 inches ;
section, 2 inches square; sharp edges i ounded
off ; weight, 21 pounds
Mr. Sturg on's original. Length round the curve,
about 1 foot ; diameter of the round bar, y 2 i'^-'h

3.91
0.196

750
fO

190
255

" The above examples are, I think, sufficient to prove the
rule I have advanced. No. 1 was probably not fully satu-
rated ; otherwise I have no doubt that its power per jj^uare
inch would have approached 800. Also the specific power
of No. 4 is small, because of the difficulty of making a good
experiment with it."

These experiments were followed by some to ascertain
the effect of the length of the iron of the magnet, whicl
he considered, at least in those cases where the degree
of magnetization is considerably below the point of
saturation, to offer a decidedly proportional resistance
to magnetization; a view the justice of which is now,
after 50 years, amply confirmed.

LECTURES ON THE ELECTROMAGNET. 45

In November of the same year further experiments 42
in the same direction were published. A tube of iron,
spirally made and welded, was prepared, planed down
as in the preceding case, and fitted to a similarly pre-
pared armature. The hollow cylinder thus formed,
shown in Fig. 8, was two feet in length. Its external
diameter was 1.42 inches, its internal being 0.5 inch.
The least sectional area was 10^ square inches. The
exciting coil consisted of a single copper rod, covered
with tape, bent into a sort of S-shape. This was later
replaced by a coil of 21 copper wires, each ^ inch in

FIG. 8. JOULE'S CYLINDRICAL ELECTROMAGNET.

diameter and 23 feet long, bound together by cotton
tape. This magnet, excited by a battery of 1C of Stur-
geon's cast-iron cells, each one foot square and one and
a half inches in interior width, arranged in a series of
four, gave a lifting power of 2,775 pounds.

Joule's work was well worthy of the master from
whom he had learned his first lesson in electromagnet-
ism. He showed his devotion not only by writing de-
&criptions of them for Sturgeon's Annals, but by exhib-
iting two of his electromagnets at the Victoria Gallery
of Practical Science, of which Sturgeon was director.
Others, stimulated into activity by Joule's example, pro-
posed new forms, among them being two Manchester

<a "Scientific Papers," p. 40, and Annals of Electricity, vol. v., p. 170.

46

LECTURES ON THE ELECTROMAGNET

gentlemen, Mr. Radford and Mr. Richard Roberts, the
latter being a well-known engineer and inventor. Mr.
^ Radford's electromagnet consisted

^P of a flat iron disc with deep spiral

grooves cut in its face, in which
were laid the insulated copper wires.
The armature consisted of a plain
iron disc of similar size. This form
is described in Vol. IV. of Sturgeon's

_

FIG. 9. ROBERTS'
TROMAGNET.

Mr. Roberts' form of electro-
magnet consisted of a rectangular
ELEC- j ron block, having straight parallel
grooves cut across its face, as in Fig.
9. This was described in Vol. VI. of Sturgeon's An-
nals, page 166. Its face was 6-f inches square and
its thickness 2 T V inches. It
weighed, with the conducting
wire, 35 pounds; and the arm-
ature, of the same size and
1| inches thick, weighed 23
pounds. The load sustained
by this magnet was no less
than 2,950 pounds. Roberts
inferred that a magnet if made
of equal thickness, but five

feet Square, Would Sustain 100 FlG " 10.-JouLB's ZIGZAG ELEC-
TROMAGNET.

tons' weight. Some of Roberts'

apparatus is still preserved in the Museum of Peel

Park, Manchester.

On page 431 of the same volume of the Annals Joule

LECTURES ON THE ELECTROMAGNET. 47

described yet another form of electromagnet, the form
of which resembled in general Fig. 10, but which, in
actual fact, was built up of 24 separate flat pieces of iron
bolted to a circular brass ring. The armature was a
similar structure, but not wound with wire. The iron
of the magnet weighed seven pounds and that of the
armature 4.55 pounds. The weight lifted was 2,710
pounds when excited by 16 of Sturgeon's cast-iron cells.

In a subsequent paper on the calorific effects of mag-
neto-electricity, 43 published in 1843, Joule described
another form of electromagnet of horseshoe shape, made
from a piece of boiler-plate. This was not intended to
give great lifting power, and was used as the field mag-
net of a motor. In 1852 another powerful electromag-
net of horseshoe form, somewhat similar to the preced-
ing, was constructed by Joule for experiment. He came
to the conclusion 44 that, owing to magnetic saturation
setting in, it was improbable that any force of electric
current could give a magnetic attraction greater than
200 pounds per square inch. " That is, the greatest
weight which could be lifted by an electromagnet formed
of a bar of iron one inch square, bent into a semicircu-
lar shape, would not exceed 400 pounds."

With the researches of Joule may be said to end the
first stage of development. The notion of the magnetic
circuit which had thus guided Joule's work did not
commend itself at that time to the professors of physi-
cal theories; and the practical men, the telegraph en-

43 "Scientific Papers," vol. i., p. 1523; and Phil. Mag., ser. iii., vol. xxiii., p.
863, 1843.
" Scientific Papers, 1 ' vol. i., p. 362; and Phil. Mag., ser. iv., vol. iii., p. 32.

48 LECTURES ON THE ELECTROMAGNET.

gineers, were for the most part content to work by
purely empirical methods. Between the practical man
and the theoretical man there was, at least on this topic,
a great gulf fixed. The theoretical man, arguing as
though magnetism consisted in a surface distribution of
polarity, and as though the laws of electromagnets were
like those of steel magnets, laid down rules not applica-
ble to the cases which occur in practice, and which
hindered rather than helped progress. The practical
man, finding no help from theory, threw it on one side
as misleading and useless. It is true that a few work-
ers made careful observations and formulated into rules
the results of their investigations. Among these, the
principal were Ritchie,, Robinson, Muller, Dub, Von
Koike, and Du Moncel; but their work was little known
beyond the pages of the scientific journals wherein their
results were described. Some of these results will be
examined in my later lectures, but they cannot be dis-
cussed in this historical resume, which is accordingly
closed.

GENERALITIES CONCERNING ELECTROMAGNETS.

Materials. In any complete treatise on the electro-
magnet it would be needful to enumerate and to discuss
in detail the several constructive features of the ap-
paratus. Three classes of material enter into its con-
struction : first, the iron which constitutes the material
of the magnetic circuit, including the armature as well
as the cores on which the coils are wound, and the yoke
that connects them; secondly, the copper which is em-
ployed as the material to conduct the electric cur-

LECTURES ON THE ELECTROMAGNET. 49

rents, and which is usually in the form of wire; thirdly,
the insulating material employed to prevent the copper
coils from coming into contact with one another, or
with the iron core. There is a further subject for dis-
cussion in the bobbins, formers, or frames upon which
the coils are in so many cases wound, and which may in
some cases be made in metal, but often are not. The
engineering of the electromagnet might well furnish
matter for a special chapter.

TYPICAL FOKMS.

It is difficult to devise a satisfactory or exhaustive
classification of the varied forms which the electromag-
net has assumed, but it is at least possible to enumerate
some of the typical forms.

1. Bar Electromagnet. This consists of a single
straight core (whether solid, tubular, or laminated), sur-
rounded by a coil. Fig. 3 depicted Sturgeon's earliest
example.

2. Horseshoe Electromagnet. There are two sub-types
included in this name. The original electromagnet of
Sturgeon (Fig. 1) really resembled a horseshoe in form,
being constructed of a single piece of round wrought
iron, about half an inch in diameter and nearly a
foot long, bent into an arch. In recent years the other
sub-type has prevailed, consisting, as shown in Fig. 11,
of two separate iron cores, usually cut from a circular
rod, fixed into a third piece of wrought iron, the yoke.
Occasionally this form is modified by the use of one coil
only, the second co v e being left uncovered. This form
has received in France the name of aimant Mteux, Its

4

50

LECTURES ON THE ELECTROMAGNET.

merits will be considered later. Sometimes a single coil
is wound upon the yoke, the two limbs being uncovered.

FIG. 11. TYPICAL TWO-POLE ELECTROMAGNKT.

3. Iron-clad Electromagnet. This form, which has
many times been re-invented, differs from the simple
bar magnet in having an iron shell
or casing external to the coils and
attached to the core at one end.
Such a magnet presents, as de-
picted in Fig. 12, a central pole at
one end surrounded by an outer
annular pole of the opposite polar-
ity. The appropriate armature for
electromagnets of this type is a cir-
cular disc or lid of iron.
FIG. 12. -IRON-CLAD ELEC- 4. Coil-and-Plunger. A de-

TROMAGNET. 1 1 L T

tached iron core is attracted into
a. hollow coil, or solenoid, of copper wire, when a om*-

LECTURES ON THE ELECTROMAGNET. 51

rent of electricity flows round the latter. This is a
special form, and will receive extended consideration.

5. Special Forms. Besides the leading forms enumer-
ated above, there are a number of special types, multi-
polar, spiral, and others designed for particular pur-
poses. There is also a group of forms intermediate
between the ordinary electromagnet and the coil-and-
plunger form.

POLARITY.

It is a familiar fact that the polarity of an electro-
magnet depends upon the sense in which the current
is flowing around it. Various rules for remembering

FIG. 13. DIAGRAM ILLUSTRATING RELATION OP MAGNETIZING CIRCUIT AND
RESULTING MAGNETIC FORCE.

the relation of the electric flow and the magnetic force
have been given. One of them that is useful is that
when one is looking at the north pole of an electromag-
net, the current will be flowing around that pole in the
sense opposite to that in which the hands of a clock are

52 LECTURES ON THE ELECTROMAGNET.

seen to revolve. Another useful rule, suggested by Max-
well, is illustrated by Fig. 13, namely, that the sense of
the circulation of the current (whether right or left
handed) and the positive direction of the resulting mag-
netic force are related together in the same way as the
rotation and the travel of a right-handed screw are as-
sociated together. Right-handed rotation of the screw
is associated with forward travel. Right-handed circu-
lation of a current is associated with a magnetic force
tending to produce north polarity at the forward end
of the core.

USES IN GENERAL.

As a piece of mechanism an electromagnet may be
regarded as an apparatus for producing a mechanical
action at a place distant from the operator who controls
it, the means of communication from the operator to
the distant point where the electromagnet is being the
electric wire. The uses of electromagnets may, how-
ever, be divided into two main divisions. For certain
purposes an electromagnet is required merely for ob-
taining temporary adhesion or lifting power. It at-
taches itself to an armature and cannot be detached so
long as. the exciting current is maintained, except by
the application of a superior opposing pull. The force
which an electromagnet thus exerts upon an armature
of iron, with which it is in direct contact, is always con-
siderably greater than the force with which it can act
on an armature at some distance away, and the two
cases must be carefully distinguished. Traction of an
armature in contact and attraction of an armature at a.

LECTURES ON THE ELECTROMAGNET. 53

distance are two different functions. So different, in-
deed, that it is no exaggeration to say that an electro-
magnet designed for the one purpose is unfitted for the
other. The question of designing electromagnets for
either of these purposes will occupy a large part of
these lectures. The action which an electromagnet ex-
ercises on an armature in its neighborhood may be of
several kinds. If the armature is of soft iron, placed
nearly parallel to the polar surfaces, the action is one
simply of attraction, producing a motion of pure trans-
lation, irrespective of the polarity of the magnet. If
the armature lies oblique to the lines of the poles there
will be a tendency to turn it round, as well as to attract
it; but, again, if the armature is of soft iron the action
will be independent of the polarity of the magnet, that
is to say, independent of the direction of the exciting
current. If, however, the armature be itself a magnet
of steel permanently magnetized, then the direction in
which it tends to turn, and the amount, or even the
sign of th force with which it is attracted, will depend
on the polarity of the electromagnet; that is to say, will
depend on the direction in which the exciting current
circulates. Hence there arises a difference between the
operation of a non-polarized and that of a polarized ap-
paratus, the latter term being applied to those forms in
which there is employed a portion say an armature
to which an initial fixed magnetization has been im-
parted. Non-polarized apparatus is in all cases inde-
pendent of the direction of the current. Another class
of uses served by electromagnets is the production of
rapid vibrations. These are employed in the median-

54 LECTURES ON THE ELECTROMAGNET.

ism of electric trembling bells, in the automatic breaks
of induction coils, in electrically driven tuning-forks
such as are employed for chronographic purposes, and
in the instruments used in harmonic telegraphy. Spe-
cial constructions of electromagnets are appropriate to
special purposes such as these. The adaptation of elec-
tromagnets for the special end of responding to rapidly
alternating currents is a closely kindred matter. Lastly,
there are certain applications of the electromagnet, no-
tably in the construction of some forms of arc lamp, for
which it is specially sought to obtain an equal, or ap-
proximately equal, pull over a definite range of motion.
This use necessitates special designs.

THE PROPERTIES OF IRON.

A knowledge of the magnetic properties of iron of
different kinds is absolutely fundamental to the theory
and design of electromagnets. No excuse is therefore
necessary for treating this matter with some fullness.
In all modern treatises on magnetism the usual terms
are defined and explained. Magnetism, which was
formerly treated of as though it were something distrib-
uted over the end surfaces of magnets, is now known
to be a phenomenon of internal structure; and the ap
propriate mode of considering it is to treat the mag-
netic materials, iron and the like, as being capable of
acting as good conductors of the magnetic lines; in
other words, as possessing magnetic permeability. The
precise notion now attached to this word is that of a
numerical coefficient. Suppose a magnetic force due,
let us say, to the circulation of an electric current in a

LECTURES ON THE ELECTROMAGNET. 55

surrounding coil were to act on a space occupied by
air: there would result a certain number of magnetic
lines in that space. In fact, the intensity of the mag-
netic force, symbolized by the letter H, is often ex-
pressed by saying that it would produce H magnetic
lines per square centimetre in air. Now, owing to the
superior magnetic power of iron, if the space subjected
to this magnetic force were filled with iron instead of
air, there would be produced a larger number of mag-
netic lines per square centimetre. This larger number
in the iron expresses the degree of magnetization in the
iron; it is symbolized 45 by the letter B. The ratio of
B and H expresses the permeability of the material.
The usual symbol for permeability is the Greek letter /*.
So we may say that B is equal to P. times H. For ex-
ample, a certain specimen of iron when subjected to a
magnetic force capable of creating, in air, 50 magnetic
lines to the square centimetre, was found to be perme-
ated by no fewer than 16,062 magnetic lines per square

45 The following are the various ways of expressing the three quantities
under consideration:

B The internal magnetization.
The magnetic induction.
The induction.

The intensity of the induction.
The permeation.

The number of lines per square centimetre in the material.
H The magnetizing force at a point.
The magnetic force at a point.
The intensity of the magnetic force.

The number of lines per square centimetre that there would be in air.
M The magnetic permeability.
The permeability.

The specific conductivity for magnetic lines.
The magnetic multiplying power of the material.

56 LECTUHES ON THE ELECTROMAGNET.

centimetre. Dividing the latter figure by the former
gives as the value of the permeability at this stage of
the magnetization 321, or the permeability of the iron
is 321 times that of air. The permeability of such non-
magnetic materials as silk, cotton, and other insulators,
also of brass, copper, and all the non-magnetic metals, is
taken as 1, being practically the same as that of the air.
This mode of expressing the fact is, however, compli-
cated by the fact of the tendency in all kinds "of iron to
magnetic saturation. In all kinds of iron the magneti-
zability of the material becomes diminished as the actual
magnetization is pushed further. In other words, when
a piece of iron has been magnetized up to a certain
degree it becomes, from that degree onward, less perme-
able to further magnetization, and though actual satu-
ration is never reached, there is a practical limit beyond
which the magnetization cannot well be pushed. Joule
was one of the first to establish this tendency toward
magnetic saturation. Modern researches have shown
numerically how the permeability diminishes as the
magnetization is pushed to higher stages. The practi-
cal limit of the magnetization, B, in good wrought iron
is about 20,000 magnetic lines to the square centimetre,
or about 125,000 lines to the square inch; and in cast
iron the practical saturation limit is nearly 12,000 lines
per square centimetre, or about 70,000 lines per square
inch. In designing electromagnets, before calculations
can be made as to the size of a piece of iron required
for the core -of a magnet for any particular purpose, it
is necessary to know the magnetic properties of that
piece of iron; for it is obvious that if the iron be of in-

LECTURES ON THE ELECTROMAGNET. 5t

ferior magnetic permeability, a larger piece of it will be
required in order to produce the same magnetic effect
as might be produced with a smaller piece of higher
permeability. Or, again, the piece having inferior per-
meability will require to have more copper wire wound
on it; for in order to bring up its magnetization to the
required point, it must be subjected to higher magnetiz-

L> 10 20 30 40 50

Fia. 14. CURVES OP MAGNETIZATION OP DIFFERENT MAGNETIC MATERIALS.

ing forces than would be necessary if a piece of higher
permeability had been selected.

A convenient mode of studying the magnetic facts
respecting any particular brand of iron is to plot on a
diagram the curve of magnetization i. e., the curve in
which the values, plotted horizontally, represent the
magnetic force H, and the values plotted vertically those
that correspond to the respective magnetization B. In
Fig. 14, which is modified from the researches of Prof.

58 LECTURES ON THE ELECTROMAGNET.

Ewing, are given five curves relating to soft iron,
hardened iron, annealed steel, hard drawn steel, and
glass-hard steel. It will be noticed that all these curves
have the same general form. For small values of H the
values of B are small, and as H is increased B increases
also. Further, the curve rises very suddenly, at least
with all the softer sorts of iron, and then bends over and
becomes nearly horizontal. When the magnetization
is in the stage below the bend of the curve, the iron is
said to be far from the state of saturation. But when
the magnetization has been pushed beyond the bend of
the curve, the iron is said to be in the stage approach-
ing saturation; because at this stage of magnetization
it requires a large increase in the magnetizing force to
produce even a very small increase in the magnetization.
It will be noted that for soft wrought iron the stage of
approaching saturation sets in when B has attained the
value of about 16,000 lines per square centimetre, or
when H has been raised to the value of about 50. As
we shall see, it is not economical to push B beyond this
limit; or, in other words, it does not pay to use stronger
magnetic forces than those of about H 50.

METHODS OF MEASURING PERMEABILITY.

There are four sorts of experimental methods of
measuring permeability.

1. Magnetometric Methods. These are due to Miiller,
and consist in surrounding a bar of the iron in question
by a magnetizing coil and observing the deflection its
magnetization produces in a rhagnetometer. '

2. Balance Methods. These methods are a variety of

LECTURES ON THE ELECTROMAGNET. 59

the preceding, a compensating magnet being employed
to balance the effect produced by the magnetized iron
on the magnetometric needle. Von Feilitzsch used this
method, and it has received a more definite applica-.
tion in the magnetic balance of Prof. Hughes. The
actual balance is exhibited to-night upon the table, and
I have beside me a large number of observations made
by students of the Finsbury Technical College by its
means upon sundry samples of iron and steel. None
of these methods are, however, to be compared with
those that follow.

3. Inductive Methods. There are several varieties of
these, but all depend on the generation of a transient
induction current in an exploring coil which surrounds
the specimen of iron, the integral current being propor-
tional to the number of magnetic lines introduced into,
or withdrawn from, the circuit of the exploring coil.
Three varieties may be mentioned.

(A) Ring Method. In this method, due to Kirch-
hoff, the iron under examination is made up into a ring,
which is wound with a primary or exciting coil arid
with a secondary or exploring coil. Determinations on
this plan have been made by Stowletow, Rowland, Bosan-
quet, and Ewing; also by Hopkinson. Rowland's ar-
rangement of the experiment is shown in Fig. 15 in
which B is the exciting battery; #, the switch for turn-
ing on or reversing the current; J?, an adjustable resist-
ance; A, an amperemeter; and B G the ballistic galva-
nometer, the first swing of which measures the integral
induced current. R C is an earth inductor or reversing
coil wherewith to calibrate the readings of the galva-

60

LECTURES ON THE ELECTROMAGNET.

nometer; and above is an arrangement of a coil and a
magnet to assist in bringing tbe swinging needle to rest
between the observations. The exciting coil and the
exploring coil are both wound upon the ring: the former
is distinguished by being drawn with a thicker line.
The usual mode of procedure is to begin with a feeble
exciting current, which is suddenly reversed, and then
reversed back. The current is then increased, reversed

FIG. 15. RING METHOD OF MEASURING PERMEABILITY (ROWLAND'S ARRANGE-
MENT).

and re-reversed; and so on, until the strongest available
points are reached. The values of the magnetizing
force H are calculated from the observed value of the
current by the following rule. If the strength of the
current, as measured by the amperemeter, be t, the num-
ber of spires of the exciting coil S and the length, in
centimetres, of the coil (i. e., the mean circumference of
the ring) be /, then H is given by the formula:

4- .Si Si

H = -- X -j- = 1.2566 X --

LECTURES ON THE ELECTROMAGNET.

Gl

Bosanquet, applying this method to a number of iron
rings, obtained some important results.

In Fig. 16 are plotted out the values of H and B for
seven rings. One of these, marked /, was of cast steel,
and was examined both when soft and afterward when
hardened. Another, marked /, was of the best Lowrnoor
iron. Five were of Crown iron, of different sizes. They
were marked for distinction with the letters G, E, F 9 H,
K. In the accompanying table are set down the values
of B at different stages of the magnetization.

TABLE OP VALUES OP B IN FIVE CROWN IRON RINGS.

Name.

G.

E.

F.

H.

K.

Mean Diameter.

21.5cm.

10.035 cm.

22.1 cm.

10.735 cm.

22.725 cm.

Bar thickness.

2.535

1.298

1.292

0.7137

0.7554

Magnetizing Force.
0.2

126

73

62

82

85

0.5

377

270

224

208

214

1

1,449

1,293

840

675

885

2

4,564

3,952

3,533

2,777

2,417

5

9.900

9,147

8.293

8,479

8,8S4

10

13,023

13,357

12,540

11,376

11.388

20

14,911

14,G53

14,710

14,066

13,273

50

16,217

15,704

16,062

15.174

13,890

100

17,148

10,077

17,900

16,134

14,837

I have the means here of illustrating the induction
method of measuring permeability. Here is an iron
ring, having a cross -section of almost exactly one square
centimetre. It is wound with an exciting coil supplied
with current by two accumulator cells ; over it is also
wound an exploring coil of 100 turns connected in cir-
cuit (as in Rowland's arrangement) with a ballistic gal-
vanometer which reflects a spot of light upon yonder
screen. In the circuit of the galvanometer is also in-
cluded a reversing earth coil, As, a matter of fact this

62

LECTURES ON THE ELECTROMAGNET.

earth coil is of such a size, and wound with so many
convolutions of wire, that when it is turned over the
amount of cutting of magnetic lines is equal to 840,000,
or is the same as if 840,000 magnetic lines had been cut
once. By adjusting the resistance of the galvanometer
circuit, it is arranged that the first swing due to the
induced current when I suddenly turn over the earth

15.000

10.000

5.000

FIG. 16. BOSANQUET'S DATA OF MAGNETIC PROPERTIES OP IRON AND STEEL

RINGS.

coil is 8.4 scale divisions. Then, seeing that our explor-
ing coil has 100 turns, it follows that when in our sub-
sequent experiment with the ring we get an induced
current from it, each division of the scale over which
the spot swings will mean 1,000 lines in the iron. I
turn on my exciting current. See: it swings about 11
divisions. On breaking the circuit it swings nearly 11
divisions, the other way. That means, that the magnetic

LECTURES ON THE ELECTROMAGNET. 63

ing force carries the magnetization of the iron up to
11,000 lines; or, as the cross-section is about one square
centimetre, B 11,000. Now, how much is H ? The
exciting coil has 180 windings, and the exciting current
through the amperemeter is just one ampere. The
total excitation is just 180 "ampere turns/' We must,
according to our rule given above, multiply this by
1.2560 and divide by the mean circumferential length of
the coil, which is about 32 centimetres. This makes H
= 7. So if B = 11,000 and H = 7, the permeability
(which is the ratio of them) is about 1,570. It is a rough
and hasty experiment, but it illustrates the method.

Bosanquet's experiments settled the debated question
whether the outer layers of an iron core shield the inner
layers from the influence of magnetizing forces. Were
this the case, the rings made from thin bar iron should
exhibit higher values of B than do the thicker rings.
This is not so; for the thickest ring, G, shows through-
out the highest magnetizations.

(B) Bar Method. This method consists in employing
a long bar of iron instead of a ring. It is covered from
end to end with the exciting coil, but the exploring coil
consists of but a few turns of wire situated just over the
middle part of the bar. Kowland, Bosanquet, and Ewing
have all employed this variety of method; and Ewing
specially used bars, the length of which was more than
100 times their diameter, in order to get rid of errors
arising from end effects.

(C) Divided Bar Method. This method, due to Dr.
Hopkinson, 46 is illustrated by Fig. 17.

* 6 JA#, Trans., 1885, p. 564,

64

LECTURES ON THE ELECTROMAGNET.

The apparatus consists of a block of annealed wrought
iron about 18 inches long, 6-i wide, and 2 deep, out of
the middle of which is cut a rectangular space to re-
ceive the magnetizing coils.

The test samples of iron consist of two rods, each
12.65 millimetres in diameter, turned carefully true,
which slide in through holes bored in the ends of the iron
blocks. These two rods meet in the middle, their ends

FIG. 17. HOPKINSON'S DIVIDED BAR METHOD OP MEASURING MAGNETIC
PERMEABILITY.

being faced true so as to make a good contact. One of
them is secured firmly, and the other has a handle fixed
to it, by means of which it can be withdrawn. The two
large magnetizing coils do not meet, a space being left
between them. Into this space is introduced the little
exploring coil, wound upon an ivory bobbin, through
the eye of which passes the end of the movable rod.
The exploring coil is connected to the ballistic galva-
nometer, B G, and is attached to an india-rubber spring
(not shown, in the figure), which, when the rod is sucl-

LECTURES ON THE ELECTROMAGNET. 65

denly pulled back, causes it to leap entirely out of the
magnetic field. The exploring coil had 350 turns of
fine wire; the two magnetizing coils had 2,008 effective
turns. The magnetizing current, generated by a bat-
tery, B, of eight Grove cells, was regulated by a variable
liquid resistance, R, and by a shunt resistance. A re-
versing switch and an amperemeter, A, were included
in the magnetizing circuit. By means of this apparatus
the sample rods to be experimented upon could be sub-
mitted to any magnetizing forces, small or large, and
the actual magnetic condition could be examined at any
time by breaking the circuit and simultaneously with-
drawing the movable rod. This apparatus, therefore,
permitted the observation separately of a series of in-
creasing (or decreasing) magnetizations without any in-
termediate reversals of the entire current. Thirty-five
samples of various irons of known chemical composition
were examined by Hopkinson, the two most important
for present purposes being an annealed wrought iron
and a gray cast iron, such as are used by Messrs. Mather
and Platt in the construction of dynamo machines.
Hopkinson embodied his results in curves, from which
it is possible to construct, for purposes of reference,
numerical tables of sufficient accuracy to serve for future
calculations. The curves of these two samples of iron
are reproduced in Fig. 18, but with one simple modifica-
tion. British engineers, who unfortunately are con-
demned by local circumstances to use inch measures
instead of the international metric system, prefer to
have the magnetic facts also stated in terms of square
inch units instead of square centimetre units. This
5

GO

LECTURES ON THE ELECTROMAGNET.

change has been made in Fig. 18, and the symbols B a
and H /y are chosen to indicate the numbers of magnetic
lines to the square inch in iron and in air respectively.
The permeability or multiplying power of the iron is

200 400 600 800 1000 1200 1400 1600

FIG. 18. CURVES OF MAGNETIZATION OF IRON.

the same, of course, in either measure. In Table II.
are given the corresponding data in square inch meas-
ure, and in Table III. the data in square centimetre
measure for the same specimens of iron.

TABLE II. (Square Inch Units.)

Annealed Wrought Iron.

Gray Cast Iron.

B a

/*

H

B,

"

HL

30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
1.10,000

4,650
3,877
3,031
2,159
1,921
1,409
9u7
408
166

6.5
10.3
16.5
27.8
36.4
56.3
99.2
245
664

25,000
30,000
40.000
50,000
60.000
70,000

763
756
258
114
74
40

32.7
39.7
155
439
807
1,480

120,000
130.000
140,000

76
35

27

1,581
3,714
5,185

:::.'.::::::"

LECTURES ON THE ELECTROMAGNET.

67

TABLE III. (Square Centimetre Units.)

Annealed Wrought Iron.

Gray Cast Iron.

B

I 1

H

B

/"

H

5,000

3,000

1.06

4,000

800

5

9,000

2,250

4

5,000

500

10

10,000

2,000

5

6,000

279

21.5

11,000

1,692

6.5

7.000

133

42

38,000

1,412

8.5

8,000

100

80

18,000

1,083

12

9,000

71

127

14,OJO

823

17

10.000

53

188

15,000

526

2S.5

11.000

37

292

16,000

320

50

17.000

161

105

18,003

90

200

19,000

54

350

20.000

6(i6

It will be noted that Hopkinson's curves are double,
there being one curve for the ascending magnetizations
and a separate one, a little above the former, for de-
scending magnetizations. This is a point of a little im-
portance in designing electromagnets. Iron, and par-
ticularly hard sorts of iron, and steel, after having been
subjected to a high degree of magnetizing force and
subsequently to a lesser magnetizing force, are found to
retain a higher degree of magnetization than if the lower
magnetizing force had been simply applied. For exam-
ple, reference to Fig. 18 shows that the wrought iron,
where subjected to a magnetizing force gradually rising
from zero to H /y = 200, exhibits a magnetization of B,,
= 95,000; but after H /y has been carried up to over
1,000 and then reduced again to 200, B /; does not come
down again to 95,000, but only to 98,000. Any sample
of iron which showed great retentive qualities, or in

68 LECTURES ON THE ELECTROMAGNET.

which the descending curve differs widely from the as-
cending curve, would be unsuitable for constructing
electromagnets, for it is important that there should be
as little residual magnetism as possible in the cores. It
will be noted that the curves for cast iron show more of
this residual effect than do those for wrought iron.
The numerical data in Tables II. and III. are means
between the ascending and descending values.

As an example of the use of the Tables we may take
the following: How strong must the magnetizing force
be in order to produce in wrought iron a magnetization
of 110,000 lines to the square inch ? Keference to Table
II. or to Fig. 18 shows that a magnetizing field of 664
will be required, and that at this stage of the magneti-
zation the permeability of the iron is only 166. As there
are 6.45 square centimetres to the square inch, 110,000
lines to the square inch corresponds very nearly to 17,-
000 lines to the square centimetre, and H /y = 664 cor-
responds very nearly to H = 100.

TRACTION METHODS.

Another group of the methods of measuring permea-
bility is based upon the law of magnetic traction. Of
these there are several varieties.

(D) Divided Ring Method. Mr. Shelford Bidwell has
kindly lent me the apparatus with which he carried out
this method. It consists of a ring of very soft charcoal
iron rod 6.4 millimetres in thickness, the external diam-
eter being eight centimetres, sawn into two half rings,
and then each half carefully wound over with an ex-
citing coil of insulated copper wire of 1,939 convolutions

LECTURES ON THE ELECTROMAGNET. 60

in' total. The two halves fit neatly together; and in
this position it constitutes practically a continuous ring.
When an exciting current is passed round the coils both
halves become magnetized and attract one another. The
force required to pull them asunder is then measured.
According to the law of traction, which will occupy us
in the second lecture, the tractive force (over a given
area of contact) is proportional to the square of the
number of magnetic lines that pass from one surface to
the other through the contact joint. Hence the force
of traction may be used to determine B; and on calcu-
lating H as before we can determine the permeability.
The following Table IV. gives a summary of Mr. Bid-
well's results :

TABLE IV. (Square Centimetre Measure.) Soft Charcoal Iron.

B

H

H

7,390

1899.1

3.9

11,550

1121.4

10.3

15,460

386.4

40

17,330

150.7

115

18,470

88.8

208

19,330

45.3

427

19,820

33.9

585

(E) Divided Rod Method. In this method, also used
by Mr. Bid well, an iron rod hooked at both ends was
divided across the middle, and placed within a vertical
surrounding magnetizing coil. One hook was hung up
to an overhead support; to the lower hook was hung a
scale pan. Currents of gradually increasing strength
were sent around the magnetizing coil from a battery
of cells, and note was taken of the greatest weight which

LECTURES ON THE ELECTROMAGNET.

could in each case be placed in the scale pan without
tearing asunder the ends of the rods.

(I 7 ) Permeameter Method. This is a method which I
have myself devised for the purpose of testing speci-
mens of iron. It is essentially a workshop method, ns
distinguished from a laboratory method. It requires no
ballistic galvanometer, and the iron does not need to be
forged into a ring or wound with a coil. For carrying it
out a simple instrument is needed,
which I venture to denominate as
a permeameter. Outwardly, it has
a general resemblance to Dr. Hop-
kinson's apparatus, and consists, as
you see (Fig. 19), of a rectangular
piece of soft wrought iron, slotted
out to receive a magnetizing coil,
down the axis of which passes a
brass tube. The block is 12 inches
long, 6^ inches wide, and 3 inches
in thickness. At one end the block
is bored to receive the sample of
iron that is to be tested. This consists simply of a
thin rod about a foot long, one end of which must be
carefully surfaced up. When it is placed inside the
magnetizing coil and the exciting current is turned on,
the rod sticks tightly at its lower end to the surface
of the iron block; and the force required to detach it
(or, rather, the square root of that force) is a measure of
the permeation of the magnetic lines through its end
face. In the first permeameter which I constructed the
magnetizing coil is 13.64 centimetres in length and has

FIG. 19. THE PERMEAME
TER.

LECTURES ON THE ELECTROMAGNET. 71

371 turns of wire. One ampere of exciting current
consequently produces a magnetizing force of H 34.
The wire is thick enough to carry 30 amperes, so that
it is easy to reach a magnetizing force of 1,000. The
current I now turn on is 25 amperes. The two rods
here are of "charcoal iron " and "best iron" respect-
ively; they are of quarter-inch square stuff. Here is a
spring balance graduated carefully, and provided with
an automatic catch so that its index stops at the highest
reading. The tractive force of the charcoal iron is
about 12-J pounds, while that of the " best" iron is only
7J pounds. B is about 19,000 in the charcoal iron, and
H being 850, /JL is about 22.3. The law of traction which
I use in calculating B will occupy us much in the next
lecture; but meantime I content myself in stating it
here for use with the permeameter. The formula for
calculating B when the core is thus detached by a pull
of P pounds, the area of contact being A square inches,
is as follows:

B = 1,317 X V P -j- A + H.

I may add that the instrument, in its final form, was
manufactured from my designs by Messrs. Nalder Bros.,
the well-known makers of so many electrical instru-
ments.

CURVES OF MAGNETIZATION AND PERMEABILITY.

In reviewing the results obtained, it will be noted that
the curves of magnetization all possess the same general
features, all tending toward a practical maximum, which,
however, is different for different materials. Joule ex-

72 LECTUKES ON THE ELECTROMAGNET.

pressed the opinion that "no force of current could gire
an attraction equal to 200 pounds per square inch/' the
greatest he actually attained being only 175 pounds per
square inch. Rowland was of opinion that the limit
was about 177 pounds per square inch for an ordinary
good quality of iron, even with infinitely great exciting
power. This would correspond roughly to a limiting
value of B of about 17,500 lines to the square centime-
tre. This value has, however, been often surpassed.
Bidwell obtained 19,820, or possibly a trifle more, as in
BidwelFs calculation the value of H has been needlessly
discounted. Hopkinson gives 18,250 for wrought iron
and 19,840 for mild Whitworth steel. Kapp gives 16,-
740 for wrought iron, 20,460 for charcoal iron in sheet,
and 23,250 for charcoal iron in wire. Bosanquet found
the highest value in the middle bit of a long bar to run
up in one specimen to 21,428, in another to 29,388, in a
third to 27,688. Ewing, working with extraordinary
magnetic power, forced up the value of B in Lowmoor
iron to 31,560 (when jj. came down to 3), and subse-
quently to 45,350. This last figure corresponds to a
traction exceeding 1,000 pounds to the square inch.

Cast iron falls far below these figures. Hopkinson,
using a magnetizing force of 240, found the values of B
to be 10,783 in gray cast iron, 12,408 in malleable cast
iron, and 10,546 in mottled cast iron. Ewing, with a
magnetizing force nearly 50 times as great, forced up
the value of B in cast iron to 31,760. Mitis metal, which
is a sort of cast wrought iron, being a wrought iron ren-
dered fluid by addition of a small percentage of alumin-
ium, is, as I have found, more magnetizable than cast

LECTURES ON THE ELECTROMAGNET. 73

iron, and not far inferior to wrought iron. It should
form an excellent material for the cores of electromag-
nets for many purposes where a cheap manufacture is
wanted.

A very useful alternative mode of studying the results
obtained by experiment is to construct curves, such as
those of Fig. 20, in which the values of the permeability

2.000
1.000

\

^

A

/

%

I

\

\$

fe,

/-

\

5

V

^

V

^

4.000 8.000 12.000 16.000 B /

FIG. 20. CUHVES OF PERMEABILITY.

are plotted out vertically in correspondence with the
values of B plotted horizontally. It will be noticed that
in the case of Hopkinson's specimen of annealed wrought
iron, between the points where B = 7,000 and B
16,000 the mean values of ;*. lie almost on a straight
line, and might be approximately calculated from the
equation :

n. = (17,000 B) -*- 3.5.

THE LAW OF THE ELECTROMAGNET.

Many attempts have been made, by Milller, Lamont,
Frolich, and others to discover a simple algebraic for-
mula whereby to express the relation between the mag-

74 LECTURES ON THE ELECTROMAGNET.

netizing force and the magnetism produced in the elec-
tromagnet. According to Midler, these are related to
one another in the same proportions as the natural
tangent is related to the arc which it subtends. The
formulae of Lament and Frolich, which are more nearly
in keeping with the facts, are based upon the assump-
tion of a relation between the permeability and the de-
gree of magnetization present. Suppose we assume the
approximation stated above, that the permeability is
proportional to the difference between B and some
higher limiting value (1 7,000 for wrought iron, 7,000 for
cast iron). If this higher value is called /? we may write

/5-B

wnere a is a constant that varies with the quality of the
iron or steel.
Now

giving by substitution and an easy transformation
B = ^,

which is one form of Frdlich's well-known formula. The
constant, a, stands for the "diacritical" value of the
magnetizing force, or that value which will bring up B
to half the assumed limiting or " satural " value..

All such formula?, however convenient, are insuffi-
cient, inasmuch as they fail to take into account the
properties of the entire magnetic circuit.

LECTURES ON THE ELECTROMAGNET.

HYSTERESIS.

I have already drawn attention to the difference be-
tween the ascending and descending curves of magneti-
zation, and may now point out that this is a part of a
set of general phenomena of residual effects. The best
known of these effects is, of course, the existence in
some kinds of iron, and notably in steel, of a remanent
or sub-permanent magnetization after the magnetizing

Fio. 21. CURVES OF HYSTERESIS.

force has been entirely removed. To this retardation
of effects behind the causes that produce them the name
of "hysteresis" has been given by Prof. Ewing. If
a piece of iron is subjected to a magnetizing force which
increases to a maximum, then is decreased down to zero,
then reversed and carried to a negative maximum, then
decreased again to zero, and so carried round an entire
cycle of magnetic operations, it is observed that the
curves of magnetization form a closed area similar in
general to those shown in Fig. 21. This closed area

LECTURES ON THE ELECTROMAGNET.

represents the work which has been wasted or dissipated
in subjecting the iron to these alternate magnetizing
forces. In very soft iron, where the ascending and de-
scending curves are close together, the inclosed area is
small, and as a matter of fact very little energy is dis-
sipated in a cycle of magnetic operations. On the other
hand, with hard iron, and particularly with steel, there
is a great width between the curves and there is a great
waste of energy. Hysteresis may be regarded as a sort
of internal or molecular magnetic friction, by reason of
which alternate magnetizations cause the iron to grow
hot. Hence the importance of understanding this curi-
ous effect, in view of the construction of electromagnets
that are to be used with rapidly alternating currents.
The following figures of Table V. give the number of
watts (one watt = -^ of a horse power) wasted by hys-
teresis in well-laminated soft wrought iron when sub-
jected to a succession of rapid cycles of magnetization.

TABLE V. WASTE OF POWER BY HYSTERESIS.

Watts wasted per

Watts wasted per

B

B

cubic foot at 10

cubic foot at 100

cycles per second.

cycles per second.

4.000

25,800

40

400

5,000

32,250

57.5

575

6,000

38,700

75

750

7,000

45,150

92.5

925

8,000 5i!eoo

111

1,110

10,000

64,500

156

1,560

12,000

77,400

206

2,060

14,000

90,300

262.

2,620

16,000

103,200

324

3,240

17,000

109,650

394

3,940

18,000

116,100

487

4,b70

It will be noted that the waste of energy increases as

LECTURES ON THE ELECTROMAGNET. 77

the magnetization is pushed higher and higher in a
disproportionate degree, the waste when B is 18,000
being six times that when B is 6,000. In the case
of hard iron or of steel the heat waste would be far
greater.

Another kind of after-effect was discovered by Ewing,
and named by him " viscous hysteresis." This is the
name given to the gradual creeping up of the magneti-
zation when a magnetic force is applied with absolute
steadiness to a piece of iron. This gradual creeping up
may go on for half an hour or more, and amount to
several per cent, of the total magnetization.

Another important matter is that all such actions as
hammering, rolling, twisting, and tlje like, impair the
magnetic quality of annealed soft iron. Annealed
wrought iron which has never been touched by a tool
shows hardly any trace of residual magnetization, even
after the application of magnetic forces. But the touch
of the file will at once spoil it. Sturgeon pointed out
the great importance of this point. In the specification
for tenders for instruments for the British Postal Tele-
graphs, it is laid down as a condition to be observed by
the constructor that the cores must not be filed after
being annealed. The continual hammering of the arma-
ture of an electromagnet against the poles may in time
produce a similar effect.

FALLACIES AND FACTS ABOUT ELECTROMAGNETS.

I will conclude this lecture by stating a few of the
fallacies that are current about electromagnets, and will

78 LECTURES ON THE ELECTROMAGNET.

add to them a few facts, some of which seem paradoxi-
cal. The refutation of the fallacies and the explanation
of the facts will come in due course.

Fallacies. The attraction of an electromagnet for its
armature varies inversely as the square of its distance
from the poles.

The outer windings of an electromagnet are neces-
sarily less effective than those that are close to the iron.

Hollow iron cores are as good as solid cores of the
same size.

Pole pieces add to the lifting power of an electro-
magnet.

It hurts an electromagnet (or, for that matter, a steel
magnet) to pull oif the keeper suddenly. [It is the sud-
den slamming on that in reality hurts it.]

The resistance of the coil of an electromagnet ought
to be equal to the resistance of the battery.

A coil wound left-handedly magnetizes a magnet dif-
ferently from a coil wound right-handedly. [It is not a
question of winding of coil, but of circulation of current.]

Thick wire electromagnets are less powerful than
thin wire electromagnets.

A badly insulated electromagnet is more powerful
than one that is well insulated.

A square iron core is less powerful (as Dal Negro says,
eighteen-fold!) than a round core of equal weight.

The attraction of an electromagnet for its keeper is
necessarily less strong (one-third according to Du Mon-
cel) sidewise than when the keeper is in front of the
poles.

Putting a tube of iron outside the coils of an electro-

LECTU'RES ON THE ELECTROMAGNET. 79

magnet makes it attract a distant armature more pow-
erfully.

Facts. A bar electromagnet with a convex pole holds
on tighter to a flat-ended armature than one with a flat
pole does.

A thin round disc of iron laid upon the flat round
end of an electromagnet (the pole end being slightly
larger than the disc), the disc is not attracted, and will
not stick on, even if laid down quite centrally.

If a flat armature of iron be presented to the poles
of a horseshoe electromagnet the attraction at a short
distance is greater, if the armature is presented flank-
wise, than if it is presented edgewise. On the contrary,
the tractive force in contact is greater edgewise than
flankwise.

Electromagnets with long limbs are practically no
better than those with short limbs for sticking on to
masses of iron.

80 LECTURES ON THE ELECTROMAGNET.

LECTURE II.

GENERAL PRINCIPLES OF DESIGN AND CONSTRUCTION
PRINCIPLE OF THE MAGNETIC CIRCUIT.

TO-NIGHT we have to discuss the law of the magnetic
circuit in its application to the electromagnet, and in
particular to dwell upon some experimental results
which have been obtained from time to time by differ-
ent authorities as to the relation between the construc-
tion of the various parts of an electromagnet and the
effect of that construction on its performance. We have
to deal not only with the size, section, length, and ma-
terial of the iron cores, and of the armatures of iron,
but we have to consider also the winding of the copper
coil and its form; and we have to speak in particular
about the way in which the shaping of the core and of
the armature affects the performance of the electromag-
net in acting on its armature, whether in contact or at
a distance. But before we enter on the last more diffi-
cult part of the subject, we will deal solely and exclu-
sively with the law of force of the magnet upon its
armature when the two are in contact with one another;
in other words, with the law of traction.

I alluded in a historical manner in my first lecture
to the principle of the magnetic circuit, telling you how
the idea had gradually grown up, perforce, from a con-

LECTURES ON THE ELECTROMAGNET. 81

sideration of the facts. The law of the magnetic cir-
cuit was, however, first thrown into shape in 1873 by
Professor Rowland, of Baltimore. He pointed out that
if you consider any simple case, and find, as electricians
do for the electric circuit, an expression for the mag-
netizing force which tends to drive the magnetism round
the circuit, and divide that by the resistance to magneti-
zation reckoned also all round the circuit, the quotient
of those two gives you the total amount of flow or flux
of magnetism. That is to say, one may calculate the
quantity of magnetism that passes in that way round
the magnetic circuit in exactly the same way as one
calculates the strength of the electric current by the law
of Ohm. Rowland, indeed, went a great deal further
than this, for he applied this very calculation to the ex-
periments made by Joule more than 30 years before, and
from those experiments deduced the degree of magnet-
ization to which Joule had driven the iron of his mag-
nets, and by inference obtained the amount of current
that he had been causing to circulate. Now, this law
requires to be written out in a form that can be used
for future calculation. To put it in words without any
symbols, we must first reckon out from the number of
turns of wire in the coil, and the number of amperes
of current which circulates in them, the whole magneto-
motive force the whole of that which tends to drive
magnetism along the piece of iron for it is, in fact,
proportional to the strength of the current and the
number of times it circulates. Next we must ascertain
the resistance which the magnetic circuit offers to the
passage of the magnetic lines. I here avowedly use
6

82 LECTURES ON THE ELECTROMAGNET.

Joule's own expression, which was afterward adopted
by Rowland, and, for short, so as to avoid having four
words, we may simply call it the magnetic resistance.
Mr. Heaviside has suggested as an advisable alternative
term magnetic reluctance., in order that we may not con-
fuse the resistance to magnetism in the magnetic cir-
cuit with the resistance to the flow of current in an
electric circuit. However, we need not quarrel about
terms ; magnetic reluctance is sufficiently expressive.
Then having found these two, the quotient of them
gives us a number representing I must not call it the
strength of the magnetic current I will call it simply
the quantity or number of magnetic lines which flow
round the circuit ; or if we could adopt a term which
is used on the continent, we might call it simply the
magnetic flux, the flux of magnetism being the analogue
of the flow of electricity in the electric law. The law
of the magnetic circuit may then be stated as follows :

magneto-motive force
- Magnetic-flux =

. reluctance.

> However, it is more convenient, to -deax. with , these
t matters in symbols, and therefore, the symbols which,!
use, and have, long been using, ought to be explained to
jou. For the number of spirals in a winding I use the
letter .$/, for . the strength of current, or number of
amperes, the letter {.; for the length of bar, or core, I
am going to use the letter I ; for the area of cross-
section, the letter A ; for the permeability of the iron
which we discussed in the last lecture, the Greek sym-
bol n; and for the total magnetic .flux, the number of

LECTURES ON THE ELECTROMAGNET. 83

magnetic lines, I use the letter N. Then our law be-
comes MS follows:

Magneto-motive f orce JQ ;
Magnetic reluctance ~" ;

Magnetic flux N = l ^

AfL

If we take the number of spirals and multiply by the
number of amperes of current, so as to get the whole
amount of circulation of electric current expressed in so
many ampere turns, and multiply by 4-, and divide by
10, in order to get the proper unit (that is to say, mul-
tiply it by 1.257), that gives us the magneto-motive
force. For magnetic reluctance, calculate out the reluc-
tance exactly as you would the resistance of an electric
conductor to the flow of electricity, or the resistance of
a conductor of heat to the flow of heat; it will be pro-
portional to the length, inversely proportional to the
cross-section, and inversely proportional to the conduc-
tivity, or, in the present case, to the magnetic permea-
bility. Now if the circuit is a simple one, we may sim-
ply write down here the length, and divide it by the
area of the cross-section and the permeability, and so
find the value of the reluctance. But if the circuit be
not a simple one, if you have not a simple ring of iron
of equal section all round, it is necessary to consider

84 LECTURES ON THE ELECTROMAGNET.

the circuit in pieces as you would an electric circuit,
ascertaining separately the reluctance of the separate
parts, and adding all together. As there may be a num-
ber of such terms to be added together, I have prefixed
the expression for the magnetic reluctance by the sign
of summation. But it does not by any means follow,
because we can write a thing down as simply as that,
that the calculation of it will be a very simple mat-
ter. In the case of magnetic lines we are quite unable
to do as one does with electric currents, to insulate the
flow. An electric current can be confined (provided we
do not put it in at 10,000 volts pressure, or anything
much bigger than that) to a copper conductor by an
adequate layer of adequately strong and I use the
word "strong" both in a mechanical and electrical sense
of adequately strong insulating material. There are
materials whose conductivity for electricity as compared
with copper may be regarded perhaps as millions of
millions of millions of times less; that is to say, they
are practically perfect insulators. There are no such
things for magnetism. The most highly insulating sub-
stance we know of for magnetism is certainly not 10,000
times less permeable to magnetism than the most highly
magnetizable substance we know of, namely, iron in its
best condition; and when one deals with electromag-
nets where curved portions of iron are surrounded with
copper, or with air, or other electrically insulating ma-
terial, one is dealing with substances whose permeability,
instead of being infinitely small compared with that of
iron, is quite considerable. We have to deal mainly
with iron when it has been well magnetized. Its per-

LECTURES ON THE ELECTROMAGNET. 85

meability competed with air is then from 1,000 to 100
roughly; that is to say, the permeability of air compared
with the iron is not less than from y^oth to y-oV^th part.
That means that it is quite possible to have a very con-
siderable leakage of magnetic lines from iron into air
occurring to complicate one's calculations and prevent
an accurate estimate being made of the true magnetic
reluctance of any part of the circuit. Suppose, how-
ever, that we have got over all these difficulties and
made our calculations of the magnetic reluctance; then
dividing the magneto-motive force by the reluctance
gives us. the whole number of magnetic lines.

There, then, is in its elementary form the law of the
magnetic circuit stated exactly as Ohm's law is stated
for electric circuits. But, as a general rule, one requires
this magnetic law for certain applications, in which the
problem is not to calculate from those two quantities
what the total of magnetic lines will be. In most of
the cases a rule is wanted for the purpose of calculating
back. You want to know how to build a magnet so as
to give you the requisite number of magnetic lines.
You start by assuming that you need to have so many
magnetic lines, and you require to know what magnetic
reluctance there will be, and how much magneto-motive
force will be needed. Well, that is a matter precisely
analogous to those which every electrician comes across.
He does not always want to use Ohm's law in the way
in which it is commonly stated, to calculate the current
from the electromotive force and the resistance; he
often wants to calculate what is the electromotive force
which will send a given current through a known resist-

86 LECTURES ON THE ELECTROMAGNET.

ance. And so do we. Our main consideration to-night
will be devoted to the question how many ampere turns
of current circulation must be provided in order to drive
the required quantity of magnetism through any given
magnetic reluctance. Therefore, we will state our law
a little differently. What we want to calculate out is
the number of ampere turns required. When once we
have got that, it is easy to say what the copper wire
must consist of, what sort of wire, and how much of it.
Turning then to our algebraic rule, we must transform
it, so as to get all the other things besides the ampere
turns to the other side of the equation. So we write
the formula:

We shall have then the ampere turns equal to the
number of magnetic lines we are going to force round
the circuit multiplied by the sum of the magnetic re-
luctances divided by 1.257. Now this number, 1.257, is
the constant that comes in when the length I is ex-
pressed in centimetres, the area in square centimetres,
and the permeability in the usual numbers. Many per-
sons unfortunately I say so advisedly because of the
waste of brain labor that they have been compelled to
go through prefer to work in inches and pounds and
feet. They have, in fact, had to learn tables instead of
acquiring them naturally without any learning. If the
lengths be specified in inches and areas in square inches,

LECTURES ON THE ELECTROMAGNET. 87

then the constant is a little different. The constant in
that case, for inch and square inch measures, is 0.3132,
so that the formula becomes:

Si= N X^-^ T X 0.3132,

Here it is convenient to leave the law of the magnetic^
circuit, and come back to it from time to time as we
require. What I want to point out before I go to any
of the applications is, that with the guidance provided
by this law, one after another the various points that
come under review can be arranged and explained, and
that there does not now remain if one applies this law
with judgment a simple fact- about electromagnets
which is either anomalous or paradoxical. Paradoxical
some things may seem in form, but they all reduce to
what is perfectly rational when one has a guiding prin-
ciple of this kind to tell you how much magnetization
you will get under given circumstances, or to tell you
how much magnetizing power you require in order to
get a given quantity of magnetization. I am using the
word " magnetization " there in the popular sense, not
in the narrow mathematical sense in which it has some-
times been used (i. e., for the magnetic moment per unit
cube of the material). I am using it simply to express
the fact that the iron or air, or whatever it may be, has
been subjected to the process which results in there
being magnetic lines of force induced through it.

Now let us apply this law of magnetic circuit in the
first place to the traction, that is to say, the lifting
power of electromagnets. The law of traction I as-

88 LECTURES ON THE ELECTROMAGNET.

sumed in my last lecture, for I made it the basis of a
method of measuring the amount of permeability. The
law of magnetic traction was stated once for all by Max-
well, in his great treatise, and it is as follows :

P (dynes) =.

87T

Where A is the area in square centimetres this be-
comes

B 2 A
P (grammes) = g _ x 9gl

That is, the pull in grammes per square centimetre
is equal to the square of the magnetic induction, B
(being the number of magnetic lines to the square cen-
timetre), divided by 8~, and divided also by 981. To
bring grammes into pounds you divide by 453.6, so that
the formula then becomes :

P (pounds) =

11,183,000 '
or if square inch measures are used :

p

P (pounds) D //

2,134,000

To save future trouble we will now calculate out from
the law of traction the following Table, in which the
traction in grammes per square centimetre or in pounds
per square inch is set down opposite the corresponding
value of B.

LECTURES ON THE ELECTROMAGNET. 89

TABLE VI. MAGNETIZATION AND MAGNETIC TRACTION.

B
lines per
sq. cm.

B u

lines per
sq. in.

Dynes
per
sq. cencim.

Grammes
per
sq. ceutnn.

Kilogrs.
per
sq. centim.

Pounds
per
sq. men.

1.000

6,450

39,790

40.56

.0456

.577

2,000

12,900 159,200

162.3

.1023

2.308

3,000

19,350 358,100

365.1

.3651

5.190

4,000

25,800

686,600

648.9

.6489

9.228

5,000

32,250

994,700

1,014

1.014

14.39

6,000

38,700

1,432,000

1,460

1.460

20.75

7,000

45,150

1,950,000

1,987

1.987

28.26

8,000

51,600

2,547,000

2,596

2.596

36.95

9,000

58,050

3,223,000

3,286

3.286

46.72

10,000

64,500

3,979,000

4,056

4.056

57.68

11,000

70,950

4,815,000

4,907

4.907

69.77

12,000

77,400

5,730,000

5,841

5.841

83.07

18,000

83,850

6,725,000

6,855

6.855

97.47

14.000

90,300

7,800.000

7,550

7.550

113.1

15,000

96,750

8,953,000

9,124

9.124

129.7

10,000

103,200

10,170,000

10,390

10.39

147.7

17,000

109,650

11,500,000

11,720

11.72

166.6

18,000

116,100

12,890,000

13,140

13.14

186.8

19,<00

122,550

14,630,000 ,

14,68C

14.63

208.1

20,000

129,000

15,920,000

16,230

16.23

230.8

This simple statement of the law of traction assumes
that the distribution of the magnetic lines is uniform
all over the area we are considering; and that unfor-
tunately is not always the case. When the distribution
is not uniform then the mean value of the squares be-
comes greater than the square of the mean value, and
consequently the pull of the magnet at its end face may,
under certain circumstances, become greater than the
calculation would lead you to expect greater than the
average of B would lead you to suppose. If the distri-
bution is not uniform over the area of contact then the
accurate expression for the tractive force (in dynes) will be

90

LECTURES ON THE ELECTROMAGNET.

To Galvanometer

20 cm .

20 cm

the integration being taken over the whole area of con-
tact.

This law of traction has been verified by experiment.
The most conclusive investigations were made about
1886 by Mr. R. H. M. Bosanquet, of Oxford, whose ap-
paratus is depicted in Fig. 22. He took two cores of

iron, well faced, and sur-
rounded them both by
magnetizing coils, fas-
tened the upper one
rigidly, and suspended
the other one on a lever
with a counterpoise
weight. To the lower
end of this core he hung
a scale-pan, and meas-
ured the traction of one
upon the other when a
known current was cir-
culating a known num-
ber of times round the
coil. At the same time
he placed an exploring
coil round the joint,
that exploring coil being connected, in the manner with
which we were experimenting last week, with a ballistic
galvanometer, so that at the moment when the two
surfaces parted company, or at the moment when the
magnetization was released by stopping the magnet-
izing current, the galvanometer indication enabled
him to say exactly how many magnetic lines went

Counterpoise

FIG. 22. BOSANQUET'S VERIFICATION OP
THE LAW OF TRACTION.

LECTURES ON THE ELECTROMAGNET. 9l

through that exploring coil. So that, knowing the
area, you could calculate the number per square centi-
metre, and you could therefore compare B 2 with the
pull per square centimetre obtained directly on the
scale-pan. Bosanquet found that even when the sur-
faces were not absolutely perfectly faced the correspond-
ence was very close indeed, not varying by more than
one or two per cent, except with small magnetizing
forces, say forces less than five 0. G. S. units.

When one knows how irregular the behavior of iron
is when the magnetizing forces are so small as this,
one is not astonished to find a lack of proportionality.
The correspondence was, however, sufficiently exact to
say that the experiments verified the law of traction,
that the pull is proportional to the square of the mag-
netic induction through the area integrated over that
area.

Now the law of traction being in that way established,
one at once begins to get some light upon the subject
of the design of electromagnets. Indeed, without going
into any mathematics, Joule had foreseen this when he
in some instinctive sort of way seemed to consider that
the proper way to regard an electromagnet for the pur-
pose of traction was to think how many square inches
of contact surface it had. He found that he could mag-
netize iron up until it pulled with a force of 175 pounds
to the square inch, and he doubted whether a traction
as great as 200 pounds per square inch could be obtained.

In the following Table Joule's results (see Table I.)
are recalculated, and the v a,lues of B deduced :

LECTURES ON THE ELECTROMAGNET.

TABLE VII. JOULE'S RESULTS RE-CALCULATED.

-- - Jteseription of
Electromagnet.

Section.

Load.

1

Is

o

a*

'

'fl

sq. in.

sq. cm.

Ibs.

kilos.

ma e g C nets..{go.3
Nesbit's

10
0.196
0.0436
0.0012
4.5
3.94
0.196

64.5
1.26
6.28
0.0077
29.1
25.3
1.26

209.0
49
12
0.202
142.8
750
53

947
22
5.4
0.09
647
346
22.6

104.5
125
137.5
81
158.5
95
127.5

7.35
8.75
9.75
5.7
11.2
6.7
8.95

13, (500
14,700
15,410
11,830
16,550
12,820
14,850

189
324

1.286
2,384
28
36
114

Henry's
Sturgeon's

I will now return to the data in Table VI., and will
ask you to compare the last column with the first.
Here are various values of B, that is to say, the amounts
of magnetization you get into the iron. You cannot
conveniently crowd more than 20,000 magnetic lines
through the square centimetre of the best iron, and, as
a reference to the curves of magnetization shows, it is
not expedient in the practical design of electromagnets
to attempt, except in extraordinary cases, to crowd more
than about 16,000 magnetic lines into the square centi-
metre. The simple reason is this : that if you are work-
ing up the magnetic force, say from up to 50, a mag-
netizing force of 50 applied to good wrought iron will
give you only 10,000 lines to the square centimetre, and
the permeability by that time has fallen to about 320,
If you try to force the magnetization any further, you
find that you have to pay for it too heavily. If you want
to force another 1,000 lines through the square centi-
metre, to go from 16,000 to 17,000, you have to add on
an enormous magnetizing force; you have to double the
whole force from that point to get another 1,000 lines

LECTURES ON THE ELECTROMAGNET 93

added. Obviously it would be much better to take a
larger piece of iron and not to magnetize it too highly
to take a piece a quarter as large again, and to mag-
netize that less forcibly. It does not therefore pay to
go much above 16,000 lines to a square centimetre
that is to say, expressing it in terms of the law of trac-
tion, and the pounds per square inch, it does not pay to
design your electromagnet so that it shall have to carry
more than about 150 pounds to the square inch. This
shall be our practical rule : let us at once take an exam-
ple, If you want to design an electromagnet to carry a
load of one ton, divide the ton, of 2,240 pounds, by 150,
and that gives the requisite number of square inches of
wrought iron, namely, 14.92, or say 15. Of course one
would work with a horseshoe shaped magnet, or some-
thing equivalent something with a return circuit and
calculate out the requisite cross-section, so that the total
area exposed might be sufficient to carry the given load
at 150 pounds to the square inch. And, as a horseshoe
magnet has two poles, the cross-section of the bar of
which it is made must be 7-J square inches. If of round
iron, it must be about 3-| inches in diameter; if of
square iron, it must be 2f inches each way.

That settles the size of the iron, but not the length.
Now, the length of the iron, if one only considers the law
of the magnetic circuit, ought to-be as short as it can
possibly be made. Reflect for what purpose we are de-
signing. The design of an electromagnet is to be con-
sidered, as every design ought to be, with a view to the
ultimate purpose to be served by that which you are
designing. The present purpose is the actual sticking

94 LECTURES ON THE ELECTROMAGNET.

on of the magnet to a heavy weight,, not acting on an-
other magnet at a distance, not pulling at an armature
separated from it by a thick layer of air; we are deal-
ing with traction in contact. The question is, How
long a piece of iron shall we need to bend over ? The
answer is: Take length enough, and no more than
enough, to permit of room for winding on the necessary
quantity of wire to carry the current which will give
the requisite magnetizing power. But this latter we do
not yet know; it has to be calculated out by the law of
the magnetic circuit. That is to say, we must calculate
the magnetic flux, and the magnetic reluctance as best
we can; then from these calculate the ampere turns of
current; and from this calculate the needful quantity
of copper wire, so arriving finally at the proper length
of the iron core. It is obvious the cross-section being
given and the value of B being prescribed, that settles
the whole number of magnetic lines, N, that will go
through the section. It is self-evident that length adds
to the magnetic reluctance, and, therefore, the longer
the length is, the greater have to be the number of
ampere turns of circulation of the current; while the
less the length is, the smaller need be the number of
ampere turns of circulation. Therefore you should de-
sign the electromagnet as stumpy as possible, that is to
say make it a stumpy arch, even as Joule did when he
came across the same problem, and arrived, by a sort of
scientific instinct, at the right solution. You should have
no greater length of iron(than is necessary in order to get
therwindings on. Then you see>we cannot absolutely
calculate the. length of the iron : tintil. we have an idea

LECTURES ON THE ELECTROMAGNET. 95

about the winding, and we must settle, therefore, pro-
visionally, about the windings. Take a simple ideal
case. Suppose we had an indefinitely long, straight iron
rod, and we wound that from end to end with a mag-
netizing coil. How thick a coil, how many ampere turns
of circulation per inch length will you require in order
to magnetize up to any particular degree ? It is a mat-
ter of very simple calculation. You can calculate ex-
actly what the magnetic reluctance of an inch length of
the core will be. For example, if you are going to mag-
netize up to 1G,000 lines per square centimetre, the per-
meability will be 320. You can take the area anything
you like, and consider the length of one inch; you can
therefore calculate the magnetic reluctance per inch of
conductor, and then you can at once say how many
ampere turns per inch would be necessary in order to
give the desired indication of 16,000 magnetic lines to
the square centimetre. And knowing the properties of
copper wire, and how it heats up when there is a cur-
rent; and knowing also how much heat you can get rid
of per square inch of surface, it is a very simple matter
to calculate what minimum thickness of copper the fire
insurance companies would allow you to use. They
would not allow you to have too thin a copper wire, be-
cause if you provide an insufficient thickness of copper
you still must drive your amperes through it to get a
sufficient number of ampere turns per inch of length ;
and if you drive those amperes through copper winding
of an insufficient thickness the copper wire will over-
heat and your insurance policy will be revoked. You
therefore are compelled, by the practical consideration

96 LECTURES ON THE ELECTROMAGNET.

of not overheating, to provide a certain thickness of
copper wire winding. I have made a rough calculation
for certain cases, and I find that for such small electro-
magnets as one may ordinarily deal with, it is not nec-
essary in any practical case to use a copper wire wind-
ing, the total thickness of which is greater than about
half an inch; and, as a matter of fact, if you use as
much thickness as half an inch, you need not then wind
the coil all along, for if you will use copper wire wind-
ing, no matter what the size, whether thin or thick, so
that the total thickness of copper outside the iron is
half an inch, you can without overheating, using good
wrought iron, make one inch of winding do for 20 inches
length of iron. That is to say, you do not really want
more than -^th. of an inch of thickness of copper out-
side the iron to magnetize up to the prescribed degree
of saturation that indefinitely long piece of which we
are thinking, without overheating the outside surface in
such a way as to violate the insurance rules. Take it
approximately, if you wind to a thickness of half an
inch the inch length of copper will magnetize 20 inches
length of iron up to the point where B equals 16,000.
If then we have a bar bent into a sort of horseshoe in
order to make it stick on to a perfectly fitting armature
also of equal section and quality, we really do not want
more than one inch along the inner curve for every 20
inches of iron. An extremely stumpy magnet, such as
I have sketched in Fig. 23, will therefore do, if one can
only get the iron sufficiently homogeneous throughout.
If, instead of crowding the wire near the polar parts,
we could wind entirely all round the curved part.

LECTURES ON THE ELECTROMAGNET. 97

though the layer of copper winding would be half an
inch thick inside the arch, it would be much less out-
side. Such a magnet, provided the armature fitted with
perfect accuracy to the polar surfaces, and provided a
battery were arranged to send the requisite number of
amperes of current through the coils, would pull with
a force of one ton, the iron being but 3| inches in diam-
eter. For my own part, in this case I should prefer not

FIG. 23. STUMPY ELECTROMAGNET.

to use round iron, one of square or rectangular section
being more convenient; but the round iron would take
less copper in winding, as each turn would be of mini-
mum length if the section were circular.

Now, this sort of calculation requires to be greatly
modified directly one begins to deal with any other case.
A stumpy short magnetic circuit with great cross-sec-
tion is clearly the right thing for the greatest traction.
You will get the given magnetization and traction with
the least amount of magnetizing force when you have
7

98 LECTURES ON THE ELECTROMAGNET.

the area as great as possible, and the length as small as
possible. You will kindly note that I have given you
as yet no proofs for the practical rales that I have been
using; they must come later. Also I have said nothing
about the size of the wire, whether thick or thin. That
does not in the least matter, for the ampere turns of
magnetizing power can be made up in any desired way.
Suppose we want on any magnet 100 ampere turns of
magnetizing power, and we choose to employ a thin wire
that will only carry half an ampere, then we must wind
200 turns of that thin wire. Or, suppose we choose to
wind it with a thick wire that will carry 10 amperes,
then we shall want only 10 turns of that wire. The
same weight of copper, heated up by the corresponding
current to an equal degree of temperature, will have
equal magnetizing power when wound on the same core.
But the rules about winding the copper will be consid-
ered later.

Now if you look in the text-books that have been
written on magnetism for information about the so-
called lifting power or portative force of magnets in
other words, the traction you will find that from the
time of Bernoulli downward, the law of portative force
has claimed the attention of experimenters, who, one
after another, have tried to give the law of portative
force in terms of the weight of the magnets; usually
dealing with permanent magnets, not electromagnets.
Bernoulli gave l a rule something of the following kind,
which is commonly known as Hacker's rule :

p = a

Helvetica, III., p. 233, 1758,

LECTURES ON THE ELECTROMAGNET. 99

where Wis the weight of the magnet, P the greatest
load it will sustain, and a a constant depending on the
unit of weight chosen, on the quality of the steel and on
its goodness of magnetization. If the weights are in
pounds, then a is found for the best steels to vary from
18 to 24 in magnets of horseshoe shape. This expres-
sion is equivalent to saying that the power which a
magnet can exert he was dealing with steel magnets;
there were no electromagnets in Bernoulli's time is
equal to some constant multiplied by the three-halfth
root of the weight of the magnet itself. The rule is
accurate only if you are dealing with a number of mag-
nets all of the same geometrical form, all horseshoes,
let us say, of the same general shape, made from the
same sort of steel, similarly magnetized. In former
years I pondered much on Hacker's rule, wondering
how on earth the three-halfth root of the weight could
have anything to do with the magnetic pull; and, hav-
ing cudgeled my brains for a considerable time, I saw
that there was really a very simple meaning in it.
What I arrived at 2 was this: If you are dealing with a
given material, say hard steel, the weight is proportional
to the volume, and the cube root of the volume is some-
thing proportional to the length, and the square of the
cube root forms something proportional to the square
of the length, that is to say, to something of the nature
of a surface. What surface ? Of course the polar sur-
face. This conTplex rule when thus analyzed turns out
to be merely a mathematician's expression of the fact
that the pull for a given material magnetized in a given

3 Philosophical Magazine, Jiily, J888,

100 LECTURES ON THE ELECTROMAGNET.

way is proportional to the area of the polar surface; a
law which in its simple form Joule seems to have ar-
rived at naturally, and which in this extraordinarily
academic form was arrived at by comparing the weights
of magnets with the weight which they would lift. You
will find it stated in many books that a good magnet
will lift 20 times its own weight. There never was a
more fallacious rule written. It is perfectly true that
a good steel horseshoe magnet weighing one pound ought
to be able to pull with a pull of 20 pounds on a properly
shaped armature. But it does not follow that a mag-
net which weighs two pounds will be able to pull with
a force of 40 pounds. It ought not to, because a mag-
net that weighs two pounds has not poles twice as big if
it is the same shape. In order to have poles twice as
big you must remember that three-halfth root coming
in. If you take a magnet that weighs eight times as
much, it will have twice the linear dimensions and four
times the surface; and with four times the surface in a
magnet of the same form, similarly magnetized, you
will have four times the pull. With a magnet eight
times as heavy you will have only four times the pull.
The pull, when other things are equal, goes by surface
and not by weight, and therefore it is ridiculous to give
a rule saying how many times its own weight a magnet
will pull. It is also narrated as a very extraordinary
thing that Sir Isaac Newton had a magnet, a loadstone,
which he wore in a signet ring, which would lift 234
times its own weight. I have had an electromagnet
which would lift 2,500 times its own weight, but then
}t was a very small one, and did not weigh more than a.

LECTURES ON THE ELECTRO AZAN!itf : ' 151'"

grain and a half. When you come to small things, of
course the surface is large proportionally to the weight;
the smaller you go, the larger becomes that dispropor-
tion. This all shows that the old law of traction in that
form was practically valueless, and did not guide you
to anything at all, whereas the law of traction as stated
by Maxwell, and explained further by the law of the
magnetic circuit, proves a most useful rule.

From this digression let us return to the law of the
magnetic circuit. I gave you in my first lecture, when
speaking of permeability, the following rule for calcu-
lating the magnetic induction B: Take the pull in
pounds, and the area of cross-section in square inches;
divide one by the other, and take the square root of the
quotient; then multiplying by 1,317 gives B; or multi-
plying by 8,494 gives B ;/ . We have therefore a means of
stepping from the pull per square inch to B //7 or from
B /x to the pull per square inch. Now the other rule of
the magnetic circuit also enables us to get from the
ampere turns down to B /; , for we have the following
expression for the ampere turns:

Si=H xS-^r- X 0.3132,
A [t

and N, the whole number of magnetic lines in the
magnetic circuit, is equal to B a multiplied by A", or

N - B.A'.

From these we can deduce a simple direct expression,
provided we assume the quality of iron as before, and
also assume that there is no magnetic leakage, and that
the area of cross-section is the same all round the cir-

16 $ LEbTlTRfeS ON THE ELECTROMAGNM.

cuit, in the armature as well as in the magnet core. So
that I" is simply the mean total path of the magnetic
lines all round the closed magnetic circuit. We may
then write :

Si = ^I_X 0.3132;
P-

whence

B, * X 8i

r X 0.3132
But by the law of traction, as stated above,

B, = 8,494 P(lbs '>
A (sq. in.)

Equating together these two values of B,, and solving,
we get for the requisite number of ampere turns of cir-
culation of exciting currents:

Si = 2,661 x X\/ P ( lbs -)
** ^(sq.in.)

This, put into words, amounts to the following rule
for calculating the amount of exciting power that is re-
quired for an electromagnet pulling at its armature, in
the case where there is a closed magnetic circuit with
no leakage of magnetic lines. Take the square root
of the pounds per square inch ; multiply this by the
mean total length (in inches) all round the iron cir-
cuit; divide by the permeability (which must be calcu-
lated from the pounds per square inch by help of Table
VI. and Table II.), and finally multiply by 2,661; the
number so obtained will be the number of ampere turns.
One goes then at once from the pull per square inch to

LECTURES Otf THE ELECTROMAGNET. 103

the number of ampere turns required to produce that
pull in a magnet of given length and of the prescribed
quality. In the case where the pull is specified in kilo-
grammes, the area of section in square centimetres, and
the length in centimetres, the formula becomes

#t = 3,951 . \/
P- v A'

As an example, take a magnet core of round annealed
wrought iron, half an inch in diameter, eight inches long,
bent to horseshoe shape. As an armature, another piece,
four inches long, bent to meet the former. Let us agree to
magnetize the iron up to the pitch of pulling with 112
pounds to the square inch. Reference to Table VI. shows
that B,, will be about 90,000, and Table II. shows that in
that case p will be about 907. From these data calculate
what load the magnet will carry, and how many ampere
turns of circulation of current will be needed.

Ans. Load (on two poles) = 43.97 Ibs.
Ampere turns needed = 372.5

N. B. In this calculation it is assumed that the contact
surface between armature and magnet is perfect. It never
is; the joint increases the reluctance of the magnetic cir-
cuit, and there will be some leakage. It will be shown later
how to estimate these effects, and to allow for them in the
calculations.

Here let me go to a matter which has been one of the
paradoxes of the past. In spite of Joule, and of the
laws of traction, showing that the pull is proportional
to the area, you have this anomaly that if you take a
bar magnet having flat-ended poles, and measure the
pull which its pole can exert on a perfectly flat arma-
ture, and then deliberately spoil the truth of the con-

104 ' LECTURES Otf TtiE ELECTROMAGNET.

tact surface, rounding it off, so making the surface gently
convex, the convex pole, which only touches at a portion
of its area instead of over the whole, will be found to
exert a bigger pull than the perfectly flat one. It has
been shown by various experimenters, particularly by
Nickles, that if you want to increase the pull of a mag-
net with armatures you may reduce the polar surface.
Old steel magnets were frequently purposely made with
a rounded contact surface. There are plenty of exam-
ples. Suppose you take a straight round core, or one
leg of a horseshoe, which answers equally, and take a
flat-ended rod of iron of the same diameter as an arma-
ture; stick it on endwise, and measure the pull when a
given amount of ampere turns of current is circulating
round. Then, having measured the pull, remove it and
file it a little, so as to reduce it at the edges, or take a
slightly narrower piece of iron, so that it will actually
be exerting its power over a smaller area, you will get a
greater pull. What is the explanation of this extraor-
dinary fact ? A fact it is, and I will show it to you.
Here, Fig. 24, is a small electromagnet which we can
place with its poles upward. This was very carefully
made, the iron poles very nicely faced, and on coming
to try them it was found they were nearly equal, bin
one pole, A, was a little stronger than the other. We
have, therefore, rounded the other pole, B, a little, and
here I will take a piece of iron, 0, which has itself been
slighty rounded at one end, though it is flat at the
other. I now turn on the current to the electromagnet,
and I take a spring balance so that we can measure the
pull at either of the two poles. When I put the flat end

LECTURES ON THE ELECTROMAGNET. I0o

of C to the flat pole A so that there is an excellent con-
tact, I find the pull about 2^ pounds. Now try the
round end of C on the flat pole A ; the pull is about
three pounds. The flat end of C on the round pole B
is also about three pounds. But if now I put together
two surfaces that are both rounded T get almost exactly
the same pull as at first with the two flat surfaces. I

FIG. 24. EXPERIMENT ON ROUND-
ING ENDS.

FIG. 25. EXPERIMENT OF DETACH-
ING ARMATURE.

have made many experiments on this, and so have
others. Take the following case: There is hung up a
horseshoe magnet, one pole being slightly convex and
the other absolutely flattened, and there is put at the
bottom a square bar armature, over which is slipped a
hook to which weights can be hung. Which end of the
armature do you think will be detached first ?

If you were going simply by the square inches, you
would say this square end will stick on tighter; it has

106 LECTtTRES ON THE ELECTROMAGNET.

more gripping surface. But, as a matter jf fact, the
other sticks tighter. Why ? We are dealing here with
a magnetic circuit. There is a certain total magnetic
reluctance all round it, and the whole number of mag-
netic lines generated in the circuit depends on two
things on the magnetizing force, and on the reluctance
all round; and, saving a little leakage, it is the same
number of magnetic lines which come through at B as
go through at A. But here, owing to the fact that
there is at B a better contact at the middle than at
the edges of the pole, the lines are crowded into a
smaller space, and therefore at that particular place B,,
the number of lines per square inch runs up higher, and
when you square the larger number, its square becomes
still larger in proportion. In comparing the square of
smaller B a with the square of greater B a , the square of
the smaller B y/ over the larger area turns out to be less
than the square of the larger B a integrated over the
smaller area. It is the law of the square coming in.

As an example, take the case of a magnet pole formed on
the end of a piece of round iron 1.15 inches in diameter.
The flat pole will have 1.05 inches area. Suppose the mag-
netizing forces are such as to make B// = 90,300, then by
Table VI. the whole pull will be 118.75 pounds, and the
actual number of lines through the contact surface will be
N = 94,815. Now suppose the pole be reduced by rounding
off the edge till the effective contact area is reduced to 0.9
square inch. If all these lines were crowded through that
area, that would give a rate of 105,350 per square inch. Sup-
pose, however, that the additional reluctance and the leak-
age reduced the number by two per cent., there would still
be 103,260 per square inch. Reference to Table VI. shows

ON THE ELECTROMAGNET.

10?

that this gives a pull of 147.7 pounds per square inch, which,
multiplied by the reduced area 0.9, gives a total pull of 132.9
pounds, which is larger than the original pull.

Let me show you yet another experiment. This is
the same electromagnet (Fig. 24) which has one flat
pole and one rounded pole. Here is an armature, also
bent, having one flat and one rounded pole. If I put
flat to flat and round to round, and pull at the middle,

FIG. 26. LINES OP FORCE RUNNING THROUGH BAR MAGNET.

the flat to flat detaches first; but if we take round to
flat and flat to round, we shall probably find they are
about equally good it is hard to say which holds the
stronger.

The law of traction can again be applied to test the
so-called distribution of free magnetism on the surface.
This is a subject on which I shall have to say a good
deal. We must therefore carefully consider what is
meant by the phrase. Let Fig, 26 be a rough drawing
of an ordinary bar magnet. Every one knows that if
we dip such a magnet into iron filings the small bits of

103 LECTURES ON THE ELECTROMAGNET.

iron stick on more especially at the ends, but not ex-
clusively, and if you hold it under a piece of paper or
cardboard, and sprinkle iron filings on the paper, you
obtain curves like those shown on the diagram. They
attest the distribution of the magnetic forces in the
external space. The magnetism running internally
through the body of the iron begins to leak out sidewise,
and, finally, all the rest leaks out in a gre.it tuft at the
end. These magnetic lines pass round to the other end
and there go in again. The place where the steel is
internally most highly magnetized is this place across
the middle, where externally no iron filings at all stick
to it. Now, we have to think of magnetism from the
inside and not the outside. This magnetism extends in
lines, coming up to the surface somewhere near the
ends of the bar, and the filings stick on wherever the
magnetism comes up to the surface. They do not stick
on at the middle part of the bar, where the metal is
really most completely permeated through and through
by the magnetism; there are a larger number of lines
per square centimetre of cross-section in the middle
region where none come up to the surface, and no filings
stick on. Now, we may explore the leakage of magnetic
lines at various points of the surface of the magnet by
the method of traction. We can thereby arrive at a
kind of measure of the amount of magnetism that is
leaking, or, if you like to call it so, of the intensity of
the "free magnetism " at the surface. I do not like to
have to use these ancient terms, because they suggest
the ancient notion that magnetism was a fluid or,
rather, two fluids, one of which was plastered on at one

LECTURES ON THE ELECTROMAGNET. 109

end of the magnet, and the other at the other, just as
you might put red paint or blue paint over the ends. I
only use that term because it is already more or less
familiar. Here is one of the ways of experimentally
exploring the so-called distribution of free magnetism.
The method was, I believe, originally due to Pliickcr;
at any rate, it was much used by him. This little piece
of apparatus was arranged by my friend and predeces-
sor, Prof. Ayrton, for the purpose of teaching his stu-
dents at the Finsbury College. 3 Here is a bar magnet
of steel, marked in centimetres from end to end ; over
the top of it there is a little steel-yard, consisting of a
weight sliding along an arm. At the end of that steel-
yard there is suspended a small bullet of iron. If we
bring that bullet into contact with the bar magnet any-
where near the end, and equilibrate the pull by sliding
the counterpoise along the steel-yard arm, we shall ob-
tain the definite pull required to detach that piece of
iron. The pull will be proportional, by Maxwell's rule,
to the square of the number of magnetic lines coming
up from the bar into it. Shift the magnet on a whole
centimetre, and attach the bullet a little further on;
now equilibrate it, and we shall find it will require a
rather smaller force to detach it. Try it again, at points
along from the end to the middle. The greatest force
required to detach it will be found at the extreme cor-
ner, and a little less a little way on, and so on until we
find at the middle the bullet does not stick on at all,
simply because there are here no magnetic lines leaking.
The method is not perfect, because it obviously depends

9 See Ayrton's "Practical Electricity, 1 ' Fig. 5a, p. 24.

110 LECTURES ON THE ELECTROMAGNET.

on the magnetic properties of the little bullet, and
whether it is much or little saturated with magnetism.
Moreover, the presence of the bullet perturbs the very
thing that is to be measured. Leakage into air is one
thing; leakage into air perturbed by the presence of the
little bullet of iron, which invites leakage into itself, is
another thing. It is an imperfect experiment at the
best, but a very instructive one. This method has
been used again and again in various cases for exploring
the apparent magnetism on the surface. I shall use it
hereafter, reserving the right to interpret the result by
the light of the law of traction.

I now pass to the consideration of the attraction of a
magnet on a piece of iron at a distance. And here I
come to a very delicate and complicated question. What
is the law of force of a magnet or electromagnet act-
ing at a point some distance away from it ? I have a
very great controversy to wage against the common way
of regarding this. The usual thing that is proper to
say is that it all depends on the law of inverse squares.
Now, the law of inverse squares is one of those detesta-
ble things needing to be abolished, which, although it
may be true in abstract mathematics, is absolutely in-
applicable with respect to electromagnets. The only
use, in fact, of the law of inverse squares, with respect
to electromagnetism, is to enable you to write an an-
swer when you want to pass an academical examination,
set by some fossil examiner, who learned it years ago at
the University, and never tried an experiment in his
life to see if it was applicable to an electromagnet. In
academical examinations they always expect you to give

LECTURES ON THE ELECTROMAGNET. Ill

the law of inverse squares. What is the law of inverse
squares ? We had better understand what it is before
we condemn it. It is a statement to the following eifect
that the action of the magnet (or of the pole, some
people say), at a point at a distance away from it, varies
inversely as the square of the distance from the pole.
There is a certain action at one inch away. Double the
distance; the square of that will be four, and, inversely,
the action will be one-quarter; at double the distance
the action is one-quarter; at three times the distance
the action is one-ninth, and so on. You just try it
with any electromagnet; nay, take any magnet you
like, and unless you hit upon the particular case, I be-
lieve you will find it to be universally untrue. Experi-
ment does not prove it. Coulomb, who was supposed
to establish the law of inverse squares by means of the
torsion balance, was working with long, thin needles of
specially hard steel, carefully magnetized, so that the
only leakage of magnetism from the magnet might be
as nearly as possible leakage in radiating tufts at the
very ends. He practically had point poles. When the
only surface magnetism is at the end faces, the magnetic
lines leak out like rays from a centre, in radial lines.
Now the law of inverse squares is never true except for
the action of points; it is a point law. If you could get
an electromagnet or a magnet with poles so small in
proportion to its length that you can consider the end
face of it as the only place through which magnetic
lines leak up into the air, and the ends themselves so
small as to be relatively mere points; if, also, you can
regard those end faces as something so far away from.

112 LECTURES ON THE ELECTROMAGNET.

whatever they are going to act upon that the distance
between them shall be large compared with their size,
and the end itself so small as to be a point, then, and
then only, is the law of inverse squares true. It is a
law of the action of points. What do we find with elec-
tromagnets ? We are dealing with pieces of iron which
are not infinitely long with respect to their cross-sec-
tion, and generally possessing round or square end faces
of definite magnitude, which are quite close to the
armature, and which are not so infinitely far away that
you can consider the polar face a point as compared
with its distance away from the object upon which it is
to act. Moreover, with real electromagnets there is
always lateral leakage; the magnetic lines do not all
emerge from the iron through the end face. Therefore,
the law of inverse squares is not applicable to that case.
What do we mean by a pole, in the first place ? We
must settle that before we can even begin to apply any
law of inverse squares. When leakage occurs all over a
great region, as shown in this diagram, every portion of
the region is polar; the word polar simply means that
you have a place somewhere on the surface of the mag-
net where filings will stick on; and if filings will stick
on to a considerable way down toward the middle, all
that region must be considered polar, though more
strongly at some parts than at others. There are some
cases where you can say that the polar distribution is
such that the magnetism leaking through the surface
acts as if there were a magnetic centre of gravity a little
way down, not actually at the end ; but cases where you
can say there is such a distribution as to have a mag-

LECTURES ON THE ELECTROMAGNET. 113

netic centre of gravity are strictly few. When Gauss
had to make up his magnetic measurements of the
earth, to describe the earth's magnetism, he found it
absolutely impossible to assign any definite centre of
gravity to the observed distribution of magnetism over
the northern regions of the earth; that, indeed, there
was not in this sense any definite magnetic pole to the
earth at all. Nor is there to our magnets. There is a

FIG. 27. APPARATUS TO ILLUSTRATE THE LAW OF INVERSE SQUARES.

polar region, but not a pole; and if there is no centre
of gravity of the surface magnetism that you can call a
pole from which to measure distance, how about the law
of inverse squares ? Allow me to show you an apparatus
(Fig. 27), the only one I ever heard of in which the law
of inverse squares is true. Here is a very long, thin
magnet of steel, about three feet long, very carefully
magnetized so as to have no leakage until quite close
up to the end. The consequence is that for practical
purposes you may treat this as. a magnet having point
8

114 LECTURES ON THE ELECTROMAGNET.

poles, about an inch away fr^m the ends. The south
pole is upward and the north pole is below, resting in
a groove in a base-board which is graduated with a scale,
and is set in a direction east and west. I use a long
magnet, and keep the south pole well away, so that it
shall not perturb the action of the north pole, which,
being small, I ask to be allowed to consider as a point.
I am going to consider this point as acting on a small
compass needle suspended over a card under this glass
case, constituting a little magnetometer. If this were
properly arranged in a room free from all other mag-
nets, and set so that that needle shall point north, what
will be the effect of having the north pole of the long
magnet at some distance eastward ? It will repel the
north end and attract the south, producing a certain de-
flection which can be read off; reckoning the force
which causes it by calculating the tangent of the angle
of the deflection. Now, let us move the north pole
(regarded as a point) nearer or farther, and study the
effect. Suppose we halve the distance from the pole to
the indicating needle, the deflecting force at half the
distance is four times as great; the force at double the
distance is one-quarter as great. Wherefore ? Because,
firstly, we have taken a case where the distance apart
is very great, compared with the size of the pole; sec-
ondly, the pole is practically concentrated at a point;
thirdly, there is only one pole acting; and fourthly,
this magnet is of hard steel, and its magnetism in no
way depends on the thing it is acting on, but is con-
stant. I have carefully made such arrangements that
the other pole shall be in the axis of rotation, so that

\ I ... I I

LECTURES ON THE ELECTROMAGNET. 115

its action on the needle shall have no horizontal com-
ponent. The apparatus is so arranged that, whatever
the position of that north pole, the south pole, which
merely slides perpendicularly up and down on a guide,
is vertically over the needle, and therefore does not tend
to turn it round in any direction whatever. With this
apparatus one can approximately verify the law of in-
verse squares. But this is not like
any electromagnet ever used for any
useful purpose. You do not make
electromagnets long and thin, with
point poles a very large distance
away from the place where they
are to act; no, you use them with
large surfaces close up to their arm-
ature.

There is yet another case which
follows a law that is not a law of in-
verse squares. Suppose you take a

bar magnet, not too long, and ap- '&-
proach it broadside on toward a FIG. SS.-DEFLECTION OF
small compass needle, Fig. 28. Of j^Z^T
course, you know as soon as you get
anywhere near the compass needle it turns round.
Did you ever try whether the effect is inversely pro-
portional to the square of the distance reckoned from
the middle of the compass needle to the middle of
the magnet? Do you think that the deflections will
vary inversely with the squares of the distances?
You will find they do not. When you place the bar
magnet like that, broadside on to the needle, the de-

116 LECTURES ON THE ELECTROMAGNET.

flections vary as the cube of the distance, not the
square.

Now, in the case of an electromagnet pulling at its
armature at a distance, it is utterly impossible to state
the law in that misleading way. The pull of the elec-
tromagnet on its armature is not proportional to the
distance, nor to the square of the distance, nor to the
cube, nor to the fourth power, nor to the square root,
nor to the three-half fch root, nor to any other power of

FIG. 29. CLOSED MAGNETIC CIRCUIT.

the distance whatever, direct or inverse, because you
find, as a matter of fact, that as the distance alters some-
thing else alters too. If your poles were always of the
same strength, if they did not act on one another, if
they were not affected by the distance in between, then
some such law might be stated. If we could always
say, as we used to say in the old language, "at that
pole," or "at that point," there are to be co-nsidered so
many " units of magnetism," and at that other place so

LECTURES Otf THE ELECTROMAGNET. 11 7

many units, and those are going to act on one another;
then you could, if you wished, calculate the force by
the law of inverse squares. But that does not corre-
spond to anything in fact, because the poles are not
points, and further, the quantity of magnetism on them
is not a fixed quantity. As soon as the iron armature
is brought near the pole of the electromagnet there is a
mutual interaction ; more magnetic lines flow out from
the pole than before, because it is easier for magnetic

FIG. 30. DIVIDED MAGNETIC CIRCUIT.

lines to flow through iron than through air. Let us
consider a little more narrowly that which happens
when a layer of air is introduced into the magnetic cir-
cuit of an electromagnet. Here we have (Fig. 29) a
closed magnetic circuit, a ring of iron, uncut, such as
we experimented on last week. The only reluctance in
the path of the magnetic lines is that of the iron, and
this reluctance we know to be small. Compare Fig. 29
with Fig. 30, which represents a divided ring with air-

118 LECTURES ON THE ELECTROMAGNET.

gaps in between the severed ends. Now, air is a less
permeable medium for magnetic lines than iron is, or,
in other words, it offers a greater magnetic reluctance.
The magnetic permeability of iron varies, as we know,
both with its quality and with the degree of magnetic
saturation. Reference to Table III. shows that if the
iron has been magnetized up so as to carry 16,000 mag-
netic lines per square centimetre, the permeability at
that stage is about 320. Iron at that stage conducts
magnetic lines 320 times better than air does; or air
offers 320 times as much reluctance to magnetic lines as
iron (at that stage) does. So then the reluctance in the
gaps to magnetization is 320 times as great as it would
have been if the gaps had been filled up with iron.
Therefore, if you have the same magnetizing coil with
the same battery at work, the introduction of air-gaps
into the magnetic circuit will, as a first effect, have the
result of decreasing the number of magnetic lines that
flow round the circuit. But this first effect itself pro-
duces a second effect. There are fewer magnetic lines
going through the iron. Consequently if there were
16,000 lines per square centimetre before, there will now
be fewer say only 12,000 or so. Now refer back to
Table III. and you will find that when B is 12,000 the
permeability of the iron is not 320, but 1,400 or so.
That is to say, at this stage, when the magnetization of
the iron has not been pushed so far, the magnetic re-
luctance of air is 1,400 times greater than that of iron,
so that there is a still greater relative throttling of the
magnetic circuit by the reluctance so offered by the air-
gaps.

LECTURES ON THE ELECTROMAGNET.

119

Apply that to the case of an actual electromagnet.
Here is a diagram, Fig. 31, representing a horseshoe
electromagnet with an armature of equal section in con-
tact with it. The actual electromagnet for the experi-
ment is here on the table. You can calculate out from
the section, the length of iron and the table of permea-

FIG. 31. ELECTROMAGNET WITH ARMA-
TURE IN CONTACT.

FIG. 32. ELECTROMAGNET WITH AIR-
GAPS ONE MILLIMETRE WIDE.

bility how many ampere turns of excitation will pro-
duce any required pull. But now consider that same
electromagnet, as in Fig. 32, with a small air-gap be-
tween the armature and the polar faces. The same
circulation of current will not now give you as much
magnetism as before, because you have interposed air-
gaps, and by the very fact of putting in reluctance there
the number of magnetic lines is reduced.

120 LECTURES ON THE ELECTROMAGNET.

Try, if you like, to interpret this in the old way by
the old notion of poles. The electromagnet has two
poles, and these excite induced poles in the opposite
surface of the armature, resulting in attraction. If
you double the distance from the pole to the iron, the
magnetic force (always supposing the poles are mere
points) will be one-quarter, hence the induced pole on
the armature will only be one-quarter as strong. But
the pole of the electromagnet is itself weaker. How
much weaker ? The law of inverse squares does not
give you the slightest clue to this all-important fact. If
you cannot say how much weaker the primary pole is,
neither can you say how much weaker the induced pole
will be, for the latter depends upon the former. The
law of inverse squares in a case like this is absolutely
misleading.

Moreover, a third effect comes in. Not only do you
cut down the magnetism by making an air-gap, but you
have a new consideration to take into account. Be-
cause the magnetic lines, as they pass up through one
of the air-gaps, along the armature, down the air-gap at
the other end, encounter a considerable reluctance, the
whole of the magnetic lines will not go that way; a lot
of them will take some shorter cut, although it may be
all through air, and you will have some leakage across
from limb to limb. I do not say you never have leakage
under other circumst mces; even with an armature in
apparent contact there is always a certain amount of
sideway leakage. It depends on the goodness of the
contact. And if you widen the air-gaps still further,
you will have still more reluctance in the path, and still

LECTURES ON THE ELECTROMAGNET.

121

less magnetism, and still more leakage. Fig. 33 roughly
indicates this further stage. The armature will be far
less strongly pulled, because, in the first place, the in-
creased reluctance strangles the flow of magnetic lines,
so that there are fewer of them in the magnetic cir-

FIG. 33.

FIG. 34.

cuit; and, in the second place, of this lesser number
only a fraction reach the armature because of the in-
creased leakage. When you take the armature entirely
away the only magnetic lines that go through the iron
are those that flow by leakage across the air from the
one limb to the other. This is roughly illustrated by
Fig. 34, the last of this set.

122 LECTURES ON THE ELECTROMAGNET.

Leakage across from limb to limb is always a waste of
the magnetic lines, so far as useful purposes are con-
cerned. Therefore it is clear that, in order to study
the effect of introducing the distance between the arma-
ture and the magnet, we have to take into account the
leakage; and to calculate the leakage is no easy matter.
There are so many considerations that occur as to that
which one has to take into account, that it is not easy
to choose the right ones and leave the wrong ones.
Calculations we must make by and by they are added
as an appendix to this lecture but for the moment ex-
periment seems to be the best guide.

I will therefore refer, by way of illustrating this ques-
tion of leakage, to some experiments made by Sturgeon.
Sturgeon had a long tubular electromagnet made of a
piece of old musket barrel of iron wound with a coil;
he put a compass needle about a foot away, and observed
the effect. He found the compass needle deflected about
23 degrees; then he got a rod of iron of equal length
and put it in at the end, and found that putting it in
so that only the end was introduced in the manner I
am now illustrating to you on the table the deflection
increased from 23 degrees to 37 degrees; but when he
pushed the iron right home into the gun barrel it went
back to nearly 23 degrees. How do you account for
that ? He had unconsciously increased its facility for
leakage when he lengthened out the iron core. And
when he pushed the rod right home into the barrel, the
extra leakage which was due to the added surface could
not and did not occur. There was additional cross-
section, but what of that ? The additional cross-section

LECTURES ON THE ELECTROMAGNET. 123

is practically of no account. You want to force the
magnetism across some 20 inches of air which resists
from 300 to 1,000 times as much as iron. What is the
use of doubling the section of the iron ? You want to
reduce the air reluctance, and you have not reduced the
air by putting a core into the tube.

There is a paradoxical experiment which we will try
next week that illustrates an important principle. If
you take a tubular electromagnet and put little pieces
of iron into the ends of the iron tube that serves as
core, and then magnetize it, the little pieces of iron will
try to push themselves out. There is always a tendency
to try and increase the completeness of the magnetic
circuit; the circuit tends to rearrange itself so as to
make it easier for the magnetic lines to go round.

Here is another paradoxical experiment. I have here
a bar electromagnet, which we will connect to the wires
that bring the exciting current. In front of it, and at
a distance from one end of the iron core, is a small com-
pass needle with a feather attached to it as a visible in-
dicator so that when we turn on the current the elec-
tromagnet will act on the needle, and you will see the
feather turn round. It is acting there at a certain dis-
tance. The magnetizing force is mainly spent not to
drive magnetism round a circuit of iron, but to force it
through the air, flowing from one end of the iron core
out into the air, passing by the compass needle, and
streaming round again, invisible, into the other end of
the iron core. It ought to increase the flow if we can
in any way aid the magnetic lines to flow through the
air. How can I aid this flow ? By putting on some-

124 LECTURES ON THE ELECTROMAGNET.

thing at the other end to help the magnetic lines to get
back home. Here is a flat piece of iron. Putting it on
here at the hinder end of the core ought to help the
flow of magnetic lines. You see that the feather makes
a rather larger excursion. Taking away the piece of
iron diminishes the effect. So also in experiments on
tractive power, it can be proved that the adding of a
mass of iron at the far end of a straight electromagnet
greatly increases the pulling power at the end that you
are working with; while, on the other hand, putting the
same piece of iron on the front end as a pole piece
greatly diminishes the pull. Here, clamped to the table,
is a bar electromagnet excited by the current, and here
is a small piece of iron attached to a spring balance by
means of which I can measure the pull required to de-
tach it. With the current which I am employing the
pull is about two and a half pounds. I now place upon
the front end of the core this block of wrought iron ; it
is itself strongly held on; but the pull which it itself
exerts on the small piece of iron is small. Less than
half a pound suffices to detach it. I now remove the
iron block from the front end of the core and place it
upon the hinder end. And now I find that the force
required to detach the small piece of iron from the
front end is about three and a half pounds instead of
two and a half pounds. The front end exerts a bigger
pull when there is a mass of iron attached to the hinder
end. Why ? The whole iron core, including its front
end, becomes more highly magnetized, because there is
now a better way for the magnetic lines to emerge at
the other end and come round to this. In short, we

LECTURES ON THE ELECTROMAGNET. 125

have diminished the magnetic reluctance of the air part
of the magnetic circuit, and the flow of magnetic lines
in the whole magnetic circuit is thereby improved. So
it was also when the mass of iron was placed across the
front end of the core; but the magnetic lines streamed
away backward from its edges, and few were left in
front to act upon the small bit of iron. So the law of
magnetic circuit action explains this anomalous behavior.
Facts like these have been well known for a long time
to those who have studied electromagnets. In Stur-
geon's book there is a remark that bar magnets pull
better if they are armed with a mass of iron at the dis-
tant end, though Sturgeon did not see what we now
know to be the explanation of it. The device of fasten-
ing a mass of iron to one end of an electromagnet in
order to increase the magnetic power of the other end
was patented by Siemens in 1862.

We are now in a position to understand the bearing
of some curious and important researches made about
40 years ago by Dr. Julius Dub, which, like a great many
other good things, lie buried in the back volumes of
Poggendorff's Annalen. Some account of them is also
given in Dr. Dub's now obsolete book, entitled "Elek-
tromagnetismus."

The first of Dub's experiments to which I will refer
relates to the difference in behavior between electro-
magnets with flat and those with pointed pole ends. He
formed two cylindrical cores, each six inches long, from
the same rod of soft iron, one inch in diameter. Either
of these could be slipped into an appropriate magnetiz-
ing coil. One of them had the end left flat, the other

126

LECTURES ON THE ELECTROMAGNET.

had its end pointed, or, rather, it was coned down until
the flat end was left only half an inch in diameter, pos-
sessing therefore only one-fourth of the amount of con-
tact surface which the other core possessed. As an
armature there was used another piece of the same soft
iron rod, 12 inches long. The pull of the electromag-
net on the armature at different distances was carefully
measured, with the following results :

Distance apart in inches.

Pull on Flat Pole

(Ibs.).

Pull on Pointed Pole
(Ibs.).

0.

3.3

5.2

0.0055

1.1

1.8

0.0110

0.9

0.75

0.0165

0.71

0.50

0.022

0.60

0.42

0.044

0.38

0.20

0.088

0.19

0.09

These results are plotted out in the curves in Fig. 35.
It will be seen that in contact, and at very short dis-
tances, the reduced pole gave the greater pull. At
about ten mils distance there was equality, but at all
distances greater than ten mils the flat pole had the
advantage. At small distances the concentration of
magnetic lines gave, in nccordance with the law of trac-
tion, the advantage to the reduced pole. But this ad-
vantage was, at the greater distances, more than out-
weighed by the fact that with the greater widths of
air-gap the use of the pole with larger face reduced the
magnetic reluctance of the gap and promoted a larger
flow of magnetic lines into the end of the armature.

Dub's next experiments relate to the employment of
polar extensions or pole-pieces attached to the core*.

LECTURES ON THE ELECTROMAGNET.

127

These experiments are so curious, so unexpected, unless
you know the reasons why, that I invite your especial
attention to them. If an engineer had to make a firm
joint between two pieces of metal, and he feared that a
mere attachment of one to the other was not adequately
strong, his first and most natural impulse would be to

20 40 60 80 100

DISTANCE IN MILS.
FIG. 35. CONTRASTED EFFECT OF FLAT AND POINTED POLES.

enlarge the parts that come together to give one, as it
were, a broader footing against the other. And that is
precisely what an engineer, if uninstructed in the true
principles of magnetism, would do in order to make an
electromagnet stick more tightly on to its armature. He
would enlarge the ends of one or both. He would add
pole-pieces to give the armature a better foothold. Noth-

128

LECTURES ON THE ELECTROMAGNET.

ing, as you will see, could be more disastrous. Dub em-
ployed in these experiments a straight electromagnet
having a cylindrical soft iron core, one inch in diameter,
twelve inches long; and as armature a piece of the same
iron, six inches long. Both were flat ended. Then six
pieces of soft iron were prepared of various sizes, to
serve as pole-pieces. They could be screwed on at will
either to the end of the magnet core or to that of the
armature. To distinguish them we will call them by
the letters A, B, 0, etc. Their dimensions were as fel-
lows, the inches being presumably Bavarian inches :

Piece.

Diameter.

Length.

A
B
C
D
E
F

Inches.
2

'1^

Inches.
1

I*

,*

2

Of the results obtained with these pieces we will select
eight. They are those illustrated by the eight collected
sketches in Fig. 36. The pull required to detach was
measured, also the attraction exerted at a certain dis-
tance apart.

Experiment.

On Magnet.

On Armature.

Traction.

Attraction.

I
II
Ill

None.
D
E

None.

None.
None.

48
30
32

22
10

11 5

IV
V
VI
VII
VIII

C
D

None.
None.
None.

None.
A
B
D
C

35

20
50
43
50

13.5

7.5
25
25
18

LECTURES ON THE ELECTROMAGNET.

129

It will be noted that, in every case, putting on a pole-
piece to the end of the magnet diminished both the pull
in contact and the attraction at a distance ; it simply
promoted leakage and dissipation of the magnetic lines.

FIG. 36. DUB'S EXPERIMENTS WITH. POLE-PIECES.

The worst case of all was that in which there were pole-
pieces both on the magnet and on the armature. In
the last three cases the pull was increased, but here the
enlarged piece was attached to the armature, so that it
helped those magnetic lines which came up into it to
9

130

LECTURES ON THE ELECTROMAGNET.

flow back laterally to the bottom end of the electromag-
net, while thus reducing the magnetic reluctance of the
return path through the air, and so, increasing the total
number of magnetic lines, did not spread unduly those
that issued up from the end of the core.

The next of Dub's results relate to the effect of add-
ing these pole-pieces to an electromagnet 12 inches
long, which was being employed,
broadside on, to deflect a distant
compass needle (Fig. 37).

Pole-piece
used.

Deflection
(degrees).

None 34.5

A 42

B 41.5

C 40 5

D 41

E 39

F 38

In another set of experiments
of the same order a permanent
magnet of steel, having polos n s,
was slung horizontally by a bifilar
suspension, to give it a strong
tendency to set in a particular
direction. At a short distance
laterally was fixed the same bar electromagnet, and
the same pole-pie.ces were again employed. The re-
sults of attaching the pole-pieces at the near end are
not very conclusive; they slightly increased the deflec-
tion. But in the absence of information as to the d.'s-
tance between the steel magnet and the electromagnet,
it is difficult to assign proper values to all the causes at
work. The results were:

FIG. 37. DUB'S DEFLECTION
EXPERIMENT.

LECTURES ON THE ELECTROMAGNET.

131

Pole-piece
used.
None. ..
A...

B

C

D...

Deflection

gB

9.2
9.5
10

When, however, the pole-pieces were attached to the
distant end of the electromagnet, where their effect
would undoubtedly be to promote the leakage of mag-

FIG. 38. DEFLECTING A STEEL MAGNET
HAVING BIFILAR SUSPENSION POLE-
PIECE ON NEAR END.

FIG. 39. DEFLECTING STEEL MAG-
NET POLE-PIECE ON DISTANT
END.

netic lines into the air at the front end without much
affecting the distribution of those lines in the space in
front of the pole, the action was more marked.

Pole-piece Deflection

10.0
10.3
10.3
104

132 LECTURES ON THE ELECTROMAGNET.

Still confining ourselves to straight electromagnets, I
now invite your attention to some experiments made in
1862 by the late Count Du Moncel as to the effect of
adding a polar expansion to the iron core. He used as
his core a small iron tube, the end of which he could
close up with an iron plug, and around which he placed
an iron ring which fitted closely on to the pole. He
used a special lever arrangement to measure the attrac-
tion exercised upon an armature distant in all cases one
millimetre from the pole. The results were as follows :

Without ring

With ring on

on pole.

pole.

Tubular core alone

11

10

" with iron p
Core provided with mass

lug

1?

27

14
25

of iron at distant end. .

with iron plug

38

33

After hunting up these researches it was extremely
interesting to find that so important a fact had not
escaped the observant eye of the original inventor of
the electromagnet. In Sturgeon's " Experimental Re-
searches " (p. 113) there is a foot note, written appar-
ently about the year 1832, which runs as follows :

"An electromagnet of the above description, weighing
three ounces, and furnished with one coil of wire, supported
14 pounds. The poles were afterward made to expose a
large surface by welding to each end of the cylindric bar a
square piece of good soft iron ; with this alteration only the
lifting power was reduced to about five pounds, although
the magnet was annealed as much as possible. "

We saw that this straight electromagnet, whether
used broadside on or end on, could act on the compass.

LECTURES ON THE ELECTROMAGNET. 133

needle at some distance from it, and deflect it. In
those experiments there was no return path for the
magnetic lines that flowed through the iron core save
that afforded by the surrounding air. The lines flowed
round in wide-sweeping curves from one end to the
other, as in Fig. 26; the magnetic field being quite ex-
tensive. Now, what will happen if we provide a return
path ? Suppose I surround the electromagnet with an
iron tube of the same length as itself, the lines will flow
along in one direction through the core, and will find
an easy path back along the outside of the coil. Will
the magnet thus jacketed pull more powerfully or less
on that little suspended magnet ? I should expect it to
pull less powerfully, for if the magnetic lines have a
good return path here through the iron tube, why should
they force themselves in such a quantity to a distance
through air in order to get home ? No, they will natu-
rally return short back from the end of the core into
the tubular iron jacket. That is to say, the action at a
distance ought to be diminished by putting on that iron
tube outside. Here is the experiment set up. And you
see that when I turn on the current my indicating
needle is scarcely affected at all. The iron jacket causes
that magnet to have much Jess action at a distance.
Yet I have known people who actually proposed to use
jacketed magnets of this sort in telegraph instruments,
and in electric motors, on the ground that they give
a bigger pull. You have seen that they produce less
action at a distance across air, but there yet remains the
question whether they give a bigger pull in contact ?
Yes, undoubtedly they do; because everything that is

134 LECTURES OK" THE ELECTROMAGNET.

helping the magnetism to get round to the other end
increases the goodness of the magnetic circuit, and
therefore increases the total magnetic flux.

We will try this experiment upon another piece of
apparatus, one that has been used for some years at the
Finsbury Technical College. It consists of a straight
electromagnet set upright in a base-board, over which is
erected a light gallows of wood. Across the frame of
the gallows goes a winch, on the axle of which ;s a
small pulley with a cord knotted to it. To the lower
end of the cord is hung a common spring balance, from
the hook of which depends a small horizontal disc of
iron to act as an armature. By means of the winch I
lower this disc down to the top of the electromagnet.
The current is turned on : the disc is attracted. On
winding up the winch I increase the upper pull until
the disc is detached. See, it required about nine pounds
to pull it off. I now slip over the electromagnet, with-
out in any way attaching it, this loose jacket of iron a
tube, the upper end of which stands flush with the
upper polar surface. Once more I lower the disc, and
this time it attaches itself at its middle to the central
pole, and at its edges to the tube. What force will now
be required to detach it ? The tube weighs about one-
half pound, and it is not fixed at the bottom. W^ill
9 pounds suffice to lift the disc ? By no means. My
balance only measures up to 24 pounds, and even that
pull will not suffice to detach the disc. I know of one
case where the pull of the straight core was -increased
16-fold by the mere addition of a good return path of
iron to complete the magnetic circuit. It is curious how

LECTURES ON THE ELECTROMAGNET. 135

often the use of a tubular jacket to an electromagnet
has been reinvented. It dates back to about 1850 and
has been variously claimed for Romershausen, for Guil-
lemin, and for Fabre. It is described in Davis" " Mag-
netism/' published in Boston in 1855. About sixteen
years ago Mr. Faulkner, of Manchester, revived it under
the name of the Altandae electromagnet. A discussion
upon jacketed electromagnets took place in 1876 at the
Society of Telegraph -Engineers; and in the same year
Professor Graham Bell used the same form of electro-
magnet in the receiver of the telephone which he exhib-
ited at the Centennial Exhibition. But the jacketed
form is not good for anything except increasing the
tractive power. Jacketing an electromagnet which
already possesses a return circuit of iron is an absurdity.
For this reason the proposal made by one inventor to
put iron tubes outside the coils of a horseshoe electro-
magnet is one to be avoided.

We will take another paradox, which equally can be
explained by the principle of the magnetic circuit. Sup-
pose you take an iron tube as an interior core; suppose
you cut a little piece off the end of it; a mere ring of
the same size. Take that little piece and lay it down
on the end. It will be struck with a certain amount of
pull. It will pull off easily. Take that same round
piece of iron, put it on edgewise, where it only touches
one point of the circumference, and it will stick on a
good deal tighter, because it is there in a position to
increase the magnetic flow of the magnetic lines. Con-
centrating the flow of magnetic lines over a small sur-
face of contact increases B at that point and B 2 , in-

136 LECTURES ON THE ELECTROMAGNET.

tegrated over the lesser area of the contact, gives a total
bigger pull than is the case when the edge is touched
all round against the edge of the tube.

Here is a still more curious experiment. I use a cyl-
indrical electromagnet set up on end, the core of which
has at the top a flat, circular polar surface, about two
inches in diameter. I now take a round disc of thin
iron ferrotype or tin-plate will answer quite well
which is a little smaller than the polar face. What will
happen when this disc is laid down flat and centrally on
the polar face ? Of course you will
say that it will stick tightly on. If
it does so, the magnetic lines which
come in through its under surface
will pass through it and come out on
its upper surface in large quantities.
It is clear that they cannot all, or even
FIG. ^.-EXPERIMENT any considerable proportion of them,
WITH TUBULAR CORE erner g e sidewise through the edges of

AND IRON RING. n

the thin disc, for there is not sub-
stance enough in the disc to carry so many magnetic
lines. As a matter of fact the magnetic lines do come
through the disc and emerge on its upper surface, mak-
ing indeed a magnetic field over its upper surface that
is nearly as intense as the magnetic field beneath its
under surface. If the two magnetic fields were exactly
of equal strength, the disc ought not to be attracted
either way. Well, what is the fact ? The fact, as you
see now that the current has been turned on, is that the
disc absolutely refuses to lie down on the top of the
pole. If I hold it down with my finger, it actually

LECTURES ON THE ELECTROMAGNET. 13?

bends itself up and requires force to keep it down. I
lift my finger, and over it flies. It will go anywhere
in its effort to better the magnetic circuit rather than
lie flat on top of the pole.

Next I invite your attention to some experiments,
originally due to Von Koike, published in the Annalen
40 years ago, respecting the distribution of the magnetic
lines where they emerge from
the polar surface of an electro-
magnet. I cannot enumerate
them all, but will merely illus-
trate them by a single exam-
ple. Here is a straight electro-
magnet with a cylindrical, flat-
ended core (Fig. 41). In what
way will the magnetic lines be
distributed over it at the end ?
Fig. 26 illustrates roughly the
way in which, when there is no
return path of iron, the mag- T

1 e FIG. 41 EXPLORING POLAR Dis-

lietlC lines leak through the TRIBOTION WITH SMALL IRON

air. The main leakage is BALL *
through the ends, though there is some at the sides
also. Now the question of the end distribution we
shall try by using a small bullet of iron, which will
be placed at different points from the middle to the
edge, a spring balance being employed to measure the
force required to detach it. The pull at the edge is
much stronger than at the middle, at least four or five
times as great. There is a regular increase of pull from
the middle to the edge. The magnetic lines, in trying

138 LECTURES ON THE ELECTROMAGNET.

to complete their own circuit, flow most numerously in
that direction where they can go furthest through iron
on their journey. They leak out more strongly at all
edges and "corners of a polar surface. They do not flow
out so strongly at the middle of the end surface, other-
wise they would have to go through a larger air circuit
to get back home. The iron is consequently more sat-
urated round the edge than at the middle; therefore,
with a very small magnetizing force, there is a great
disproportion between pull at the middle and that at
the edges. With a very large magnetizing force you do
not get the same disproportion, because if the edge is
already far saturated you cannot by applying higher
magnetizing power incrsase its magnetization much,
but you can still force more lines through the middle.
The consequence is, if you plot out the results of a suc-
cession of experiments of the pull at different points,
the curves obtained are, with larger magnetizing forces,
more nearly straight than are those obtained with small
magnetizing forces. I have known cases where the pull
at the edge was six or seven times as great as in the
middle with a small magnetizing power, but with larger
power not more than two or three times as great, al-
though, of course, the pull all over was greater You
can easily observe this distinction by merely putting a
polished iron ball upon the end of the electromagnet, as
in Fig. 42. The ball at once rolls to the edge and will
not stay at the middle. If I take a larger two-pole
electromagnet (like Fig. 11), what will the case now be?
Clearly the shortest path of the magnetic lines through
the air is the path just across from the edge of one

LECTURES ON THE ELECTROMAGNET.

139

polar surface to the edge of the other between the

poles. The lines are most dense in the region where

they arch over in as short an arch as possible, and they

will be less dense along the

longer paths, which arch more

widely over. Therefore, as

there is a greater tendency to

leak from the inner edge of

one pole to the inner edge of

the other, and less tendency

to leak from the outer edge of

one to the outer edge of the

other, the biggest pull ought _

FIG. 42. IRON BALL ATTRACTED
to be On the inner edges of TO EDGE OF POLAR FACE.

the pole. We will now try it.

On putting the iron ball anywhere on the pole it im-
mediately rolls until it stands perpendicularly over the
inner edge.

The magnetic behavior of little iron balls is very curi-
ous. A small round piece of iron does not tend to move
at all in the most powerful magnetic field if that mag-
netic field is uniform. All that a small ball of iron
tends to do is to move from a place where the magnetic
field is weak to a place where the magnetic field is
strong. Upon that fact depends the construction of
several important instruments, and also certain pieces
of electromagnetic mechanism.

In order to study this question of leakage, and the
relation of leakage to pul], still more incisively, I de-
vised some time ago a small experiment with which a
group of my students at the Technical College have

140

LECTURES ON THE ELECTROMAGNET.

been diligently experimenting. Here (Fig. 43) is a
horseshoe electromagnet. The core is of soft wrought
iron, wound with a known number of turns of wire. It
is provided with an armature. We have also wound on
three little exploring coils, each consisting of five turns
of wire only, one, C, right down at the bottom on the
bend; another, B, right round the pole, close up to the
armature, and a third, A, around the middle of the arma-
ture. The object of these
is to ascertain how much
of the magnetism which
was created in the core by
the magnetizing power of
these coils ever got into the
armature. If the armature
is at a considerable distance
away, there is naturally a
great deal of leakage. The
coil C around the bend at
the bottom is to catch all
the magnetic lines that go
through the iron; the coil
B at the poles is to catch all that have not leaked outside
before the magnetism has crossed the joint; while the
coil J, right around the middle of the armature, catches
all the lines that actually pass into the armature, and
pull at it. We measure by means of the ballistic gal-
vanometer and these three exploring coils how much
magnetism gets into the armature at different distances,
and are able thus to determine the leakage, and compare
these amounts with the calculations made, and with the

FIG. 43. EXPERIMENT ON LEAKAGE
OF ELECTROMAGNET.

LECTURES ON THE ELECTROMAGNET.

141

attractions at different distances. The amount of mag-
netism that gets into the armature does riot go by a law
of inverse squares, I can assure you, but by quite other
laws. It goes by laws which can only be expressed as
particular cases of the law of the magnetic circuit. The
most important element of the calculations, indeed, in
many cases is the amount of percentage of leakage that
must be allowed for. Of the magnitude of this matter
you will get a very good idea by the result of these ex-
periments following.

The iron core is 13 millimetres in diameter, and the
coil consists of 178 turns. The first swing of the gal-
vanometer when the current was suddenly turned on or
off measured the number of magnetic lines thereby sent
through, or withdrawn from, the exploring coil that is
at the time joined to the galvanometer. The currents
used varied from 0.7 of an ampere to 5.7 amperes. Six
sets of experiments were made, with the armature at
different distances. The numerical results are given
below :

I. WITH WEAK CURRENT (0.7 AMPERE).

A

s

C

In contact

12506

13 870

14 190

f

1 mm

1 552

2 103

3 786

* 8 J

2 mm

1,149

1 487

2 839

si* si

5 mm

1 014

1 081

2 028

4 *h

Removed

Omm

67G

1,014 .
675

1,690
1 352

142 LECTURES ON THE ELECTROMAGNET.

II. STRONGER CURRENT (1.7 AMPERES).

In contact . . 18,240 19,590 20 283

, 1mm 2,570 3.381 5,408

i] 2mm 2,366 2,839 5,073

5mm 1)352 2j2 99 5949

1 10 mm 811 1,352 3,381

Removed ... 1,308 3,041

III. STILL STRONGER CURRENT (3.7 AMPERES).

A B C

In contact 20,940 22,280 22,960

lmm 5,610 7,568 11,831

38! 2mm 4 5 97 6,722 9,802

I 5 mm 2,569 3,245 7,436

-> 110 mm 1,149 2,704 7,098

Removed 2,366 6,427

IV. STRONGEST CURRENT (5.7 AMPERES).

A B C

In contact 21.980 23,660 24,040

f 1mm 8,110 10,810 17,220

2mm 5,611 8,464 15,886

5mm 4,056 5,273 12,627

[10 mm 2,029 4,057 10,142

Removed 3,581 9,795

These numbers may be looked upon as a kind of
numerical statement of the facts roughly depicted in
Figs. 31 to 34. The numbers themselves, so far as they
relate to the measurements made (1) in contact, (2) with
gaps of one millimetre breadth, are plotted out on Fig.
44, there being three curves, A, B and (7, for the meas-
urements m^de when the armature was in contact,, and

LECTURES ON THE ELECTROMAGNET.

143

three others, A\, BI, C\, made at the one millimetre dis-
tance. A dotted line gives the plotting of the numbers
for the coil C, with different currents, when the arma-
ture was removed.

On examining the numbers in detail we observe that
the largest number of magnetic lines forced round the
bend of the iron core, through the coil C, was 24,040
(the cross-section being a little over one square centi-

W.ooc

tb.ooo

'100 500 1000

FIG. 44. CURVES OF MAGNETIZATION PLOTTED FROM PRECEDING.

metre), which was when the armature was in contact.
When the armature was away the same magnetizing
power only eVoked 9,795 lines. Further, of those 24,-
040, 23,660 (or 98^ per cent.) came up through the polar
surfaces of contact, and of those again 21,980 (or 92| per
cent, of the whole number) passed through the arma-
ture. There was leakage, then, even when the armature
was in contact, but it amounted to only 7-j- per cent.
Now, when the armature was moved but one millimetre

144 LECTURES ON THE ELECTROMAGNET.

(i. e., one twenty-fifth of an inch) away, the presence of
the air-gaps had this great effect, that the total mag-
netic flux was at once choked down from 24,040 to 17,-
220. Of that number only 10,810 (or 61 per cent.)
reached the polar surfaces, and only 8,110 (or 47 per
cent, of the total number) succeeded in going through
the armature. The leakage in this case was 53 per
cent. ! With a two millimetre gap the leakage was 65
per cent, when the strongest current was used. It was
68 per cent, with a five millimetre gap, and 80 per cent,
with a 10 millimetre gap. It will further be noticed
that while a current of 0.7 ampere sufficed to send 12,-
506 lines through the armature when it was in contact,
a current eight times as strong could only succeed in
sending 8,110 lines when the armature was distant by a
single millimetre.

Such an enormous diminution in the magnetic flux
through the armature, consequent upon the increased
reluctance and increased leakage occasioned by the pres-
ence of the air-gaps, proves how great is the reluctance
offered by air, and how essential it is to have some prac-
tical rules for calculating reluctances and estimating
leakages to guide us in designing electromagnets to do
any given duty.

The calculation of magnetic reluctances of definite
portions of a given material are now comparatively
easy, and, thanks to the formulae of Prof. Forbes, it is
now possible in certain cases to estimate leakages. Of
these methods of calculation an abstract will be given
in the appendix to this lecture. I have, however, found
Forbes' rules, which were intended to aid the design of

LECTURES ON THE ELECTROMAGNET. 145

dynamo machines, not very convenient for the common
cases of electromagnets, and have therefore cast about
to discover some more apposite mode of calculation. To
predetermine the probable percentage of leakage one
must first distinguish between those magnetic lines
which go usefully through the armature (and help to
pull it) and those which go astray through the sur-
rounding air and are wasted so far as any pull is con-
cerned. Having set up this distinction, one then needs
to know the relative magnetic conductance, or permeance,
along the path of the useful lines, and that along the
innumerable paths of the wasted lines of the stray field.
For (as every electrician accustomed to the problems
of shunt circuits will recognize) the quantity of lines
that go respectively along the useful and wasteful paths
will be directly proportional to the conductances (or
permeances) along those paths, or will be inversely pro-
portional to the respective resistances along those paths.
It is customary in electromagnetic calculations to em-
ploy a certain coefficient of allowance for leakage, the
symbol for which is v, such that when we know the
number of magnetic lines that are wanted to go through
the armature we must allow for v times as many in the
magnet core. Now, x if u represents permeance along the
useful path, and w the permeance of all the waste paths
along the stray field, the total ftux will be to the use-
ful Rux as u -|- w is to u. Hence the coefficient of
allowance for leakage v is equal to u -\- w divided by u.
The only real difficulty is to calculate u and w. In gen-
eral u is easily calculated; it is the reciprocal of the
sum of all the mngnetic reluctances along the useful
10

146

LECTURES ON THE ELECTROMAGNET.

path from pole to pole. In the case of the electromag-
net used in the experiments last described, the magnetic
reluctances along the useful path are three in number,
that of the iron of the armature and those of the two
air-gaps. The following formula is applicable,

h

reluctance =

4-

if the data are specified in centimetre measure, the suf-
fixes 1 and 2 relating respectively to the iron and to the
air. If the data are specified in inch measures the for-
mula becomes

reluctance = 0.3132

/ A" ' A'-
\ JH if*i J

But it is not so easy to calculate the reluctance (or its
reciprocal, the permeance) for the
waste lines of the stray field, be-
cause the paths of the magnetic
lines spread out so extraordinarily
and bend round in curves from
pole to pole.

Fig. 45 gives a very fair repre-
sentation of the spreading of the
lines of the stray field that leaks
across between the two limbs of a
horseshoe electromagnet made of
round iron. And for square iron
the flow is much the same, except
that it is concentrated a little by
the corners of the metal. Forbes 7 rules do not help us
here. We want a new mode of considering the subject.

FIG. 45. CURVES OF FLOW
OP MAGNETIC LINES IN AIR
FROM ONE CYLINDRICAL,
POLE TO ANOTHER.

LECTURES ON THE ELECTROMAGNET. 147

The problems of flow, whether of heat, electricity or
of magnetism, in space of three dimensions, are not
among the most easy of geometrical exercises. How-
ever, some of them have been worked out, and may be
made applicable to our present need. Consider, for
example, the electrical problem of finding the resistance
which an indefinitely extended liquid (say a solution of
sulphate of copper of given density) offers when acting
as a conductor of electric currents flowing across between
two indefinitely long parallel cylinders of copper. Fig.
45 may be regarded as representing a transverse section
of such an arrangement, the sweeping curves represent-
ing lines of flow of current. In a simple case like this
it is possible to find an accurate expression for the re-
sistance (or of the conductance) of a layer or stratum of
unit thickness. It depends on the diameters of the
cylinders, on their distance apart, and on the specific
conductivity of the medium. It is not by any means
proportional to the distance between them, being, in
fact, almost independent of the distance, if that is
greater than 20 times the perimeter of either cylinder.
Neither is it even approximately proportional to the
perimeter of the cylinders except in those cases when
the shortest distance between them is less than a tenth
part of the perimeter of either. The resistance, for
unit length of the cylinders, is, in fact, calculated out
by the rather complex formula :

R = log. nat. h;
Where

n =

148

LECTURES ON THE ELECTROMAGNET.

1i4( . r r I-

the symbol a standing for the radius of the cylinder; b
for the shortest distance separating them; /j. for the
permeability, or in the electric case the specific conduc-
tivity of the medium.

Now, I happened to notice, as a matter that greatly
simplifies the calculation, that if we confine our atten-
tion to a transverse layer of the medium of given thick-
ness, the resistance be-
tween the two bits of the
cylinders in that layer
depends on the ratio of
the shortest distance sep-
arating them to their
periphery, and is inde-
pendent of the absolute
size of the system. If
you have the two cylin-
ders an inch round and
an inch between them,
then the resistance of the
slab of medium (of given
thickness) in which they
lie will be the same as if

they were a foot round and a foot apart. Now that sim-
plifies matters very much, and thanks to my friend and
former chief assistant, Dr. R. Mullineux Walmsley, who
devoted himself to this troublesome calculation, I am
able to give you, in tabular form, the magnetic resist-
ances within the limits of proportion that are likely to
occur.

FIG. 46. DIAGRAM OF LEAKAGE RE-
LUCTANCES.

LECTURES ON THE ELECTROMAGNET.

140

TABLE VIII. MAGNETIC RELUCTANCE OF AIR BETWEEN Two PARALLEL
CYLINDRICAL LIMBS OF IRON.

6

Magnetic reluctance in C. G.
S. units = the magneto-mo-

Magnetic reluctance in inch
units the ampere turns -f-

P
Ratio of least

tive force -*- total magnetic
flux.

the total magnetic flux.
Slab = 1 inch thick.

distance apart

to perimeter.

Reluctance.

Permeance.

Reluctance.

Permeance.

0.1

0.2461

4.063

0.0771

12.968

0.2

0.3404

2.938

0.1066

9.377

0.3

0.4084

2.449

0.1280

7.815

0.4

0.4628

2.161

0.1450

6.897

0.5

0.5084

1.967

0.1593

6.278

0.6

0.5479

1.825

0.1717

5.825

0.8

0.6140

1.629

0.1924

5.198

1.0

0.6681

1.497

0.2093

4.777

1.2

0.7144

1.400

0.2238

4.571

1.4

0.7550

1.324

0.2365

4.228

16

0.7903

1.265

0.2476

4.039

1.8

0.8220

1.217

0.257o

3.883

2.0

0.8511

1.202

0.2667

3.750

4.0

1.0500

0.952

0.3290

3.040

6.0

1.1710

0.854

0.3669

2.726

8.0

1.2624

0.792

0.3955

2.528

10

1.3250

0.755

0.4151

2.409

NOTE. In the above table, unit length of cylinders is assumed (1 centimetre
in columns 2 and 3 ; 1 inch in columns 4 and 5) ; the flow of magnetic lines
being reckoned as in a slab of infinite extent and of unit thickness. Sym-
bols : p = perimeter of cylinder ; b = shortest distance between cylinders.
In columns 2 and 3 the unit reluctance is that of a centimetre cube of air. In
columns 4 and 5 the unit reluctance is so chosen (as in the rest of these lec-
tures wherever such measures are used) that the reduction of ampere turns
to magneto-motive force by multiplying by4n--r-10 is avoided. This will
make the reluctance of the inch cube of air equal to 10 -s- 4w -s- 2.54 = 0.3132,
and its permeance as 3.1931.

The numbers from columns 1 and 2 of the preceding
table are plotted out graphically in Fig. 46 for more
convenient reference. As an example of the use of the
table we will take the following :

EXAMPLE. Find the magnetic reluctance and permeance
between two parallel iron cores of one inch diameter and

150 LECTURES ON THE ELECTROMAGNET.

nine inches long, the least distance between them being 2$-
inches. Here b = 2.375; p = 3.1416; b H- p = 0.756. Refer-
ence to the table shows (by interpolation) that the reluc-
tance and permeance for unit thickness of slab are respect-
ively 0.183 and 5.336. For nine inches thickness they will
therefore be 0.021 and 48.02 respectively.

"When the permeance across between the two limbs is
thus approximately calculable, the waste flux across the
space is estimated by multiplying the permeance so
found by the average value of the difference of magnetic
potential between the two limbs. And this, if the yoke
which unites the limbs at their lower end is of good
solid iron, and if the parallel cores offer little magnetic
reluctance as compared with the reluctance of the use-
ful paths, or of that of the stray field, may be simply
taken as half the ampere turns (or, if centimetre meas-
ures are used, multiply by 1.2566).

The method here employed in estimating the reluc-
tance of the waste field is of course only an approxima-
tion; for it assumes that the leakage takes place only in
the planes of the slabs considered. As a matter of fact
there is always some leakage out of the planes of the
slabs. The real reluctance is always therefore some-
what less, and the real permeance somewhat greater,
than that calculated from Table VIII.

For the electromagnets used in ordinary telegraph
instruments the ratio of b to p is not usually very dif-
ferent from unity, so that for them the permeance across
from limb to limb per inch length of core is not very
far from 5.0, or nearly twice the permeance of an inch
cube of air.

LECTURES Otf THE ELECTROMAGNET. 151

We are now in a position to see the reason for a curi-
ous statement of Count Du Moncel which for long puz-
zled me. He states that he found, using distance apart
of one millimetre, that the attraction of a two-pole elec-
tromagnet for its armature was less when the armature
was presented laterally than when it was placed in front
of the pole-ends, in the ratio of 19 to 31. He does not
specify in the passage referred to what was the shape
of either the armature or the cores. If we assume that
he was referring to an electromagnet with cores of the
usual sort round iron with flat ends, presumably like
Fig. 11 then it is evident that the air-gaps, when the
armature is presented sidewise to the magnet, are really
greater than when the armature is presented in the
usual way, owing to the cylindric curvature of the core.
So, if at equal measured distance the reluctance in the
circuit is greater, the magnetic flux will be less and the
pull less.

It ought also now to be evident why an armature
made of iron of a flat rectangular section, though when
in contact it sticks on tighter edgewise, is at a distance
attracted more powerfully if presented flatwise. The
gaps, when it is presented flatwise (at an equal least dis-
tance apart), offer a lesser magnetic reluctance.

Another obscure point also becomes explainable,
namely, the observation by Lenz, Barlow, and others,
that the greatest amount of magnetism which could be
imparted to long iron bars by a given circulation of
electric current was (nearly) proportional, not to the
cross-sectional area of the iron, but to its surface! The
explanation is this: Their magnetic circuit was a bad

LECTURES ON THE ELECTROMAGNET.

30.2<

one, consisting of a straight rod of iron and of a return
path through air. Their magnetizing force was being
in reality expended not so much on 'driving magnetic
lines through iron (which is readily permeable), but on
driving the magnetic lines through air (which is, as we
know, much less permeable), and the reluctance of the
return paths through the air is when the distance
from one to the other of the exposed end parts of the
bar is great compared with its per-
iphery very nearly proportional to
that periphery, that is to say, to the
exposed surface.

Another opinion on the same topic
was that of Prof. Miiller, who laid
down the law that for iron bars of
equal length, and excited by the
same magnetizing power, the amount
of magnetism was proportional to
the square root of the periphery. A
vast amount of industrious scientific
effort has been expended by Dub,
Hankel, Von Feilitzsch, and others
on the attempt to verify this " law." Not one of these ex-
perimenters seems to have had the faintest suspicion that
the real thing which determined the amount of mag-
netic flow was not the iron, but the reluctance of the re-
turn path through air. Von Feilitzsch plotted out the
accompanying curves (Fig. 47), from which he drew the
inference that the law of the square root of the periphery
was established. The very straightness of these curves
shows that in no case had the iron become so much

FIG. 47. VON FEI-
LITZSCH'S CURVES OF
MAGNETIZATION op
RODS OF VARIOUS
DIAMETERS.

LECTURES ON THE ELECTROMAGNET. 153

magnetized as to show the bend that indicates approach-
ing saturation. Air, not iron, was offering the main
part of the resistance to magnetization in the whole of
these experiments. I draw from the very same curves
the conclusion that the magnetization is not propor-
tional to the square root of the periphery, but is more
nearly proportional to the periphery itself; indeed, the
angles at which the different curves belonging to the
different peripheries rise show that the amount of mag-
netism is very nearly as the surface. Observe here we
are not dealing with a closed magnetic circuit where
section comes into account; we are dealing with a bar
in which the magnetism can only get from one end to
the other by leaking all round into the air. If, there-
fore, the reluctance of the air path from one end of the
bar to the other is proportional to the surface, we should
get some curves very like these ; and that is exactly
what happens. If you have a solid, of a certain given
geometrical form, standing out in the middle of space,
the conductance which the space around it (or rather
the medium filling that space) offers to the magnetic
lines flowing through it, is practically proportional to
the surface. It is distinctly so for similar geometrical
solids, when they are relatively small as compared with
the distance between them. Electricians know that the
resistance of the liquid between two small spheres, or
two small discs of copper immersed in a large bath of
sulphate of copper, is practically independent of the
distance between them, provided they are not within
ten diameters, or so, of one another. In the case of a
long bar we may treat the distance between the protrud-

154 LECTtTHES ON THE ELECTROMAGNET.

ing ends as sufficiently great to make an approximation
to this law hold good. Von Feilitzsch's bars were, how-
ever, not so long that the average value of the length of
path from one end surface to the other end surface,
along the magnetic lines, was infinitely great as com-
pared with the periphery. Hence the departure from
exact proportionality to the surface. His bars were 9.1
centimetres long, and the peripheries of the six were
respectively 94.9, 90.7, 79.2, 67.6, 54.9 and 42.9 millime-
tres.

It has long been a favorite idea with telegraph en-
gineers that a long-legged electromagnet in some way
possessed a greater " protective " power than a short-
legged one; that, in brief, a long-legged magnet could
attract an armature at a greater distance from its poles
than could a short-legged one made with iron cores of
the same section. The reason is not far to seek. To
project or drive the magnetic lines across a wide inter-
vening air-gap requires a large magnetizing force on
account of the great reluctance, and the great leakage
in such cases. And the great magnetizing force cannot
be got with short cores, because there is not, with short
cores, a sufficient length of iron to receive all the turns
of wire that are in such a case essential. The long leg
is wanted simply to carry the wire necessary to provide
the requisite circulation of current.

We now see how, in designing electromagnets, the
length of the iron core is really determined; it must be
long enough to allow of the winding upon it of the wire
which, without overheating, will carry the ampere turns
of exciting current which will suffice to force the requi-

LECTURES Otf THE ELECTROMAGNET. 155

site number of magnetic lines (allowing for leakage)
across the reluctances in the useful path. We shall
come back to this matter after we have settled the mode
of calculating the quantity of wire that is required.

Being now in a position to calculate the additional
magnetizing power required for forcing magnetic lines
across an air-gap, we are prepared to discuss a matter
that has been so far neglected, namely, the effect on the
reluctance of the magnetic circuit of joints in the iron.
Horseshoe electromagnets are not always made of one
piece of iron bent round. They are often made, like
Fig. 11, of two straight cores shouldered and screwed, or
riveted into a yoke. It is a matter purely for experi-
ment to determine how far a transverse plane of section
across the iron obstructs the flow of magnetic lines.
Armatures, when in contact with the cores, are never
in perfect contact, otherwise they would cohere without
the application of any magnetizing force; they are only
in imperfect contact, and the joint offers a considerable
magnetic reluctance.

This matter has been examined by Prof. J. J. Thom-
son and Mr. Newall, in the Cambridge Philosophical
Society's Proceedings, in 1887; and recently more fully
by Prof. Ewing, whose researches are published in the
Philosophical Magazine for September, 1888. Ewing
not only tried the effect of cutting and of facing up
with true plane surfaces, but used different magnetizing
forces, and also applied various external pressures to the
joint. For our present purpose we need not enter into
the questions of external pressures, but will summarize
the results which Ewing found when his bar of wrought

156

LECTURES ON THE ELECTROMAGNET.

iron was cut across by section planes, first into two
pieces, then into four, then into eight. The apparent
permeability of the bar was reduced at every cut.

TABLE IX. EFFECT OF JOINTS IN WROUGHT IRON BAR (NOT COMPRESSED).

Mean thickness of

Thiekness of iron

B

equivalent air-
space for one

of equivalent
reluctance per

H

cut.

cut.

Solid.

Cut in
two.

In
four.

In
eight.

Centi-
metres.

Inches.

Centi-
metres.

Inches.

7.5

8,500

6,900

4,809

2,600

0.0036

0.0014

4.

1.57

15

13,400

11,550

8,900

5,550

0.0030

0.0012

2.53

1.00

80

15,350

14,550

12,940

9,800

0.0020

0.0008

1.10

0.433

50

16,400

15,950

15,000

13,300

0.0013

0.0005

0.43

0.169

70

17,100

16,840

16,120

15,200

0.0009

0.0004

0.22

0.087

Suppose we are working with the magnetization of
our iron pushed to about 16,000 lines to the square cen-
timetre (i. e. y about 150 pounds per square inch, trac-
tion), requiring a magnetizing force of about H = 50;
then, referring to the table, we see that each joint
across the iron offers as much reluctance as would an
air-gap 0.0005 of an inch in thickness, or adds as much
reluctance as if an additional layer of iron about one-
sixth of an inch thick had been added. With small
magnetizing forces the effect of having a cut across the
iron with a good surface on it is about the same as
though you had introduced a layer of air one six-hun-
dredth of an inch thick, or as though you had added to
the iron circuit about one inch of extra length. With
large magnetizing forces, however, this disappears, prob-
ably because of the attraction of the two surfaces across
that cut. The stress in the magnetic circuit with high

LECTURES ON THE ELECTROMAGNET.

157

magnetic forces running up to 15,000 or 20,000 lines to
the square centimetre will of itself put on a pressure of
130 to 230 pounds to the square inch, and so these resist-
ances are considerably reduced; they come down in fact
to about one-twentieth of their initial value. When
Ewing specially applied compressing forces, which were
as large as 670 pounds to the square inch, which would
of themselves ordinarily, in a continuous piece of iron,
have diminished the mag-
netizability, he found the
diminution of the magnet-
izability of iron itself was
nearly compensated for by
the better conduction of
the cut surface. The old
sn rf ace, cut and compressed
in that way, closes up as
it were, magnetically -
does not act like a cut at
all; but at the same time
you lose just as much as you
gain, because the iron itself
becomes less magnetizable.

The above results of Swing's are further represented
by the curves of magnetization drawn in Fig. 48. When
the faces of a cut were carefully surfaced up to true
planes, the disadvantngeous effect of the cut was re-
duced considerably, find, under the application of a heavy
external pressure, almost vanished.

I have several times referred to experimental results
obtained in past years, principally by German and

FIG. 48. SWING'S CURVES FOR EFFECT
OF JOINTS.

158 LECTURES ON THE ELECTROMAGNET.

French workers, buried in obscurity in the pages of
foreign scientific journals. Too often, indeed, the
scattered papers of the German physicists are rendered
worthless or unintelligible by reason of the omission of
some of the data of the experiments. They give no
measurements perhaps of their currents, or they used
an uncalibrated galvanometer, or they do not say how
many windings they were using in their coils ; or per-
haps they give their results in some obsolete phraseol-
ogy. They are extremely addicted to informing you
about the " magnetic moments " of their magnets. Now
the magnetic moment of an electromagnet is the one
thing that one never wants to know. Indeed the mag-
netic moment of a magnet of any kind is a useless piece
of information, except in the case of bar magnets of
hard steel that are to be used in the determination of
the horizontal component of the earth's magnetic force.
What one does want to know about an electromagnet
is the number of magnetic lines flowing through its cir-
cuit, and this the older researches rarely afford the
means of ascertaining. Nevertheless, there are some
investigations worthy of study to which time will now
only permit me very briefly to allude. These are the
researches of Dub on the effect of thickness of arma-
tures, and those of Nickles and of Du Moncel on the
lengths of armatures. Also those of Nickles on the
effect of width between the two limbs of the horseshoe
electromagnet.

I can only now describe some experiments of Von
Feilitzsch upon the vexed question of tubular cores, a
matter touched by Sturgeon, Pfaff, Joule, Nickles, and

LECTURES ON THE ELECTROMAGNET.

159

later by Du Moncel. To examine the question whether
the inner part of the iron really helps to carry the mag-
netism, Von Feilitzsch prepared a set of thin iron tubes
which could slide inside one another. They were all
11 centimetres long, and their peripheries varied from
6.12 centimetres to 9.7 centimetres. They could be
pushed within a magnetizing spiral to which either
small or large currents could be applied, and their effect
in deflecting a magnetic needle was
noted, and balanced by means of a
compensating steel magnet, from
the position of which the forces
were reckoned and the magnetic
moments calculated out. As the
tubes were of equal lengths, the
magnetization is approximately
proportional to the magnetic mo-
ment. The outermost tube was

u 240 a jo

first placed in the spiral, and a set

, .. -IT ,-,,-, FIG. 49. VON FEILITZSCH'S

of observations made; then the tube CURVES OP MAGNKTIZA-
of next smaller size was slipped TION OF TuBES -
into it and another set of observations made; then
a third tube was slipped in until the whole of the
seven were in use. Owing to the presence of the outer
tube in all the experiments, the reluctance of the air
return paths was alike in every case. The curves given
in Fig. 49 indicate the results.

The lowest curve is that corresponding to the use of
the first tube alone. Its form, bending over and be-
coming nearly horizontal, indicates that with large
magnetizing power it became nearly saturated. The

(MAGNETIZATION POWER

160 LECTURES ON THE ELECTROMAGNET.

second curve corresponds to the use of the first tube
with the second within it. With greater section of iron
saturation sets in at a later stage. Each successive tube
adds to the capacity for carrying magnetic lines, the
beginning of saturation being scarcely perceptible, even
with the highest magnetizing power, when all seven
tubes were used. All the curves have the same initial
slope. This indicates that with small magnetizing
forces, and when even the least quantity of iron was
present, when the iron was far from saturation, the
main resistance to magnetization was that of the air
paths, and it was the same whether the total section of
iron in use was large or small.

I must leave till my next lecture the rules relating to
the determination of the windings of copper wire on
the cores.

LECTURES ON THE ELECTROMAGNET. 161

APPENDIX TO LECTURE II.
CALCULATION OF EXCITATION, LEAKAGE, ETC.

Symbols used.

N = the whole number of magnetic lines (C.G. S. defini-
tion of magnetic lines, being one line per square
centimetre to represent intensity of a magnetic
field, such that there is one dyne on unit magnetic
pole) that pass through the magnetic circuit.
Also called the magnetic flux.

B = the number of magnetic lines per square centi-
metre in the iron; also called the induction* or
the internal magnetization.

B /7 = the number of magnetic lines per square inch
in the iron.

H the magnetic force or intensity of the magnetic
field, in terms of the number of magnetic lines
to the square centimetre that there would be in
air.

H^ the magnetic force, in terms of the number of
magnetic lines that there would be to the square
inch, in air.

P. = the permeability of the iron, etc. ; that is its mag-
netic conductivity or multiplying power for mag-
netic lines.

A = area of cross-section, in square centimetres.
ii

162 LECTURES ON THE ELECTROMAGNET.

A" = area of cross-section, in square inches.

I = length, in centimetres.

I" = length, in inches.

8 = number of spirals or turns in the magnetizing

coil.

i = electric current, expressed in amperes.
v = coefficient of allowance for leakage; being the

ratio of the whole magnetic flux to that part of

it which is usefully applied. (It is always greater

than unity.)

Relations of units.

1 inch = 2.54 centimetres;

1 centimetre 0.3937 inch.

1 square inch = 6.45 square centimetres;

1 square centimetre = 0.1550 square inch.

1 cubic inch 16.39 cubic centimetres ;

1 cubic centimetre = 0.0610 cubic inch.

To calculate the value of B or of B^from the traction.

If P denote the pull, and A the area over which it
is exerted, the following formulae (derived from Max-
welFs law) may be used :

B = 4,965 A 7 J kilos '

A sq. cm.'

B = 1,316.6 \/

v

A sq. in. 9

- .

A s. m,

r

LECTURES ON THE ELECTROMAGNET. 163

To calculate the requisite cross-section of iron for a given
traction.

Reference to p. 89 will show that it is not expedient
to attempt to employ tractive forces exceeding 150
pounds per square inch in magnets whose cores are of
soft wroughfc iron, or exceeding 28 pounds per square
inch in cast iron. Dividing the given load that is to be
sustained by the electromagnet by one or other of these
numbers gives the corresponding requisite sectional
area of wrought or cast iron respectively.

To calculate the permeability from B or from B^.

This can only be satisfactorily done by referring to a
numerical Table (such as Table II. or IV.), or to graphic
curves, such as Fig. 18, in which are set down the re-
sult of measurements made on actual samples of iron of
the quality that is to be used. The values of IJL for the
two specimens of iron to which Table II. refers may
be approximately calculated as follows :

^ 17,000 - B

For annealed wrought iron, // = - ;

3.5

7,000 - B

For gray cast iron, /JL = .

3.2

These formulae must not be used for the wrought
iron for tractions that are less than 28 pounds per
square inch, nor for cast iron for tractions less than 2%
pounds per square inch,

164 LECTUBES ON THE ELECTROMAGNET.

To calculate the total magnetic flux which a core of
given sectional area can conveniently carry.

It has been shown that it is not expedient to push
the magnetization of wrought iron heyond 100,000
lines to the square inch, nor that of cast iron beyond
42,000. These are the highest values that ought to be
assumed in designing electromagnets. The total mag-
netic flux is calculated by multiplying the figure thus
assumed by the number of square inches of sectional
area.

To calculate the magnetizing power requisite to force a
given number of magnetic lines through a definite
magnetic reluctance.

Multiply the number which represents the magnetic
reluctance by the total number of magnetic lines that
are to be forced through it. The product will be the
amount of magneto-motive force. If the magnetic re-
luctance has been expressed on the basis of centimetre
measurements, the magneto-motive force, calculated as

above, will need to be divided by 1.2566 ft. e. t by ^j

to give the number of ampere turns of requisite magnet-
izing power. If, however, the magnetic reluctance has
been expressed in the units explained below, based
upon inch measures, the magnetizing power, calculated
by the rule given above, will already be expressed
directly in ampere turns,

LECTURES ON THE ELECTROMAGNET. 165

To calculate the magnetic reluctance of an iron core.

(a.) If dimensions are given in centimetres. Mag-
netic reluctance being directly proportional to length,
and inversely proportional to sectional area and to per-
meability, the following is the formula :

Magnetic reluctance - ;

A p.

but the value of /JL cannot be inserted until one knows
how great B is going to be; when reference to Table II.
gives fj..

(b.) If dimensions are given in inches. In this case
we can apply a numerical coefficient, which takes into
account the change of units (2.54), and also, at the
same time, includes the operation of dividing the mag-
neto-motive force by T 4 ^ of TT ( = 1.2566) to reduce it to
ampere turns. 80 the rule becomes

V

Magnetic reluctance = -^ X 0.3132.

Example. Find the magnetic reluctance from end to end
of a bar of wrought iron 10 inches long, with a cross-section
of 4 square inches, on the supposition that the magnetic
flux through it will amount to 440,000.

To calculate the total magnetic reluctance of a mag-
netic circuit.

This is done by calculating the magnetic reluctances
of the separate parts, and adding them together. Ac-
count must, however, be taken of leakage; for when the
flux divides, part going through an armature, part

166

LECTURES ON THE ELECTROMAGNET.

through a leakage path, the law of shunts comes in, and
the net reluctance of the joint paths is the reciprocal of
the sum of their reciprocals, In the simplest case the
magnetic circuit consists of three parts, (1) armature,
(2} air in the two gaps, (3) core of the magnet. These
three reluctances may be separately written thus:

For Centimetre Measure.

For Inch Measure.

1A vrnflturp

h

1"
v 31 3

2. The gaps.

Aim
2 h

A ifj-i
1"

9 \/ fl Q1 Q9

3. Magnet core. . .

8 ~3T

k

A -rjj- X U.oio/s

A 2

-in

v 31 3'>

^3/'-3

ttt A U.OlO/v
A 3/^3

If the iron used in armature and core is of the same
quality, and magnetized up to the same degree of satu-
ration, //-i and /j-s will be alike. For the air-gaps /j. = 1,
and therefore is not written in.

If there were no leakage, the total reluctance would
simply be the sum of these three terms. But when
there is leakage, the total reluctance is reduced.

To calculate the ampere turns of magnetizing power req-
uisite to force the desired magnetic flux through the
reluctances of the magnetic circuit,
(a.) If dimensions are given in centimetres the rulo is:
Ampere turns = the magnetic flux, multiplied by the

magnetic reluctance of the circuit, divided by T 4 of n

(= 1.2566).

LECTURES ON THE ELECTROMAGNET. 167

Or, in detail, the three separate amounts of ampere
turns required for three principal magnetic reluctances
are explained as follows :

Ampere turns required to ) 7 A*

drive N lines through iron > = N X

of armature )

Ampere turns required to ) 07

drive N lines through the [ = N X - -^ ,

two gaps ) ^2

Ampere turns required to ) 7 4r

drive vH lines through the > = vN x ; -,

iron of magnet core ) ^ 3//3

And, adding up :

Total ampere turns re- ( 7 07 7 ^

. _ 10 _. 3_A_ + ^!L -H-J^-t.

quired = N | AM A 2 r A&* \

(b.) If dimensions are given in inches, the rule is :
Ampere turns = magnetic flux multiplied by the
magnetic reluctance of the circuit.
Or, in detail :

Ampere turns required to } ^"

drive N lines through iron >- = N X-TF~ X 0.3132,

of armature ) ^ 1/^-1

Ampere turns required to ) o?//

drive N lines through two V = N X -~T- X 0.3132.

gaps )

Ampere turns required to ) -^

drive vH lines through iron > = vH X nrX 0.3132;

core of magnet ) -<* V*a

And, adding up :

Total ampere turns re- j l"\ 2^2 , vl's ]

quired = 0.3132N ( ~A\^ Tl 1 ," T 3Va ) '

168 ' LECTURES ON THE ELECTROMAGNET.

It will be noted that here v, the coefficient of allow-
ance for leakage, has been introduced. This has to be
calculated as shown later. In the mean time it may be
pointed out that, in designing electromagnets for any
case where v is approximately known beforehand, the
calculation may be simplified by taking the sectional
area of the magnet core greater than that of the arma-
ture in the same proportion. For example, if it were
known that the waste lines that leak were going to be
equal in number to those that are usefully employed in
the armature (here v 2), the iron of the cores might
be made of double the section of that of the armature.
In this case // 3 will approximately equal ni.

To calculate tlie coefficient of allowance for leakage, v.

v = total magnetic flux generated in magnet core -j-
useful magnetic flux through armature. The respective
useful and waste magnetic fluxes are proportional to the
permeances along their respective paths. Permeance,
or magnetic conductance, is the reciprocal of the re-
luctance, or magnetic resistance. Call useful permeance
through armature and gaps u; and the waste permeance
in the stray field w; then

u -f- w

v =

u

w may be estimated by the Table VIII. or other leakage
rules, but should be divided by 2 as the average differ-
ence of magnetic potential over the leakage surface is only
about half that at the ends of the poles.

LECTURES ON THE ELECTROMAGNET. 169

RULES FOR ESTIMATING MAGNETIC LEAKAGE.
(I. to III. adapted from Prof. Forbes 7 rules.)

Prop. I. Permeance between two parallel areas facing
one another. Let areas be A\ and A< square inches,
and distance apart d" inches, then :

Permeance = 3.193 X i (A'\ + A'*) -r- d".

Prop. II. Permeance between two equal adjacent rect-
angular areas lying in one plane. Assuming lines of
flow to be semicircles, and that distances d" \ and d"%
between their nearest and furthest edges respectively
are given, also a" their width along the parallel edge:

Permeance = 2.274-. X a" X logio^4--

Prop. III. Permeance between two equal parallel rect-
angular areas lying in one plane at some distance apart.
Assume lines of leakage to be quadrants joined by
straight lines.

Permeance = 2.274 X a" X lo glo j 1 + !lilZ^Ll j.

Prop. IV. Permeance between two equal areas at
right angles to one another.

Permeance (if air angle is 90) double the respect-
ive value calculated by II. or III.

Permeance (if air angle is 270) = two-thirds times
the respective value calculated by II.

1^0 LECTURES ON THE ELECTROMAGNET.

If measures are given in centimetres these rules be-
come the following :

I. At A + d

III.

Prop. V. Permeance between two parallel cylinders of
indefinite length.

The formula for the reluctance is given above: the
permeance is the reciprocal of it. Calculations are sim-
plified by reference to Table VIII.

LECTURES ON THE ELECTROMAGNET. 171

LECTUKE III.

SPECIAL DESIGNS.

IN continuation of my lecture of last week I have to
make a few remarks before entering upon the consider-
ation of special forms of magnets which was to form the
entire topic of to-night's lecture. I had not quite fin-
ished the experimental results which related to the per-
formance of magnets under various conditions. I had
already pointed out that where you require a magnet
simply for holding on to its armature common sense (in
the form of our simplest formula) dictated that the cir-
cuit of iron should be as short as was compatible with
getting the required amount of winding upon it. That
at once brings us to the question of the difference in
performance of long magnets and short ones. Last week
we treated that topic so far as this, that if you require
your magnet to attract over any range across an air
space you require a sufficient amount of exciting power
in the circulation of electric current to force the mag-
netic lines across that resistance, and therefore you re-
quire length of core in order to get the required coil
wound upon the magnetic circuit. But there is one

1?2 LECTURES ON THE ELECTROMAGNET.

other way in which the difference of behavior between
long and short magnets I am speaking of horseshoe
shapes comes, into play. So far back as 1840, Ritchie
found it was more difficult to magnetize steel magnets
(using for that purpose electromagnets to stroke them
with) if those electromagnets were short than if they
were long. He was of course comparing magnets which
had the same tractive power, that is to say, presumably
had the same section of iron magnetized up to the same
degree of magnetization. This difference between long
and short cores is obviously to be explained on the same
principle as the greater projecting power of the long-
legged magnets. IH order to force magnetism not only
through an iron arch, but through whatever is beyond,
which has a lesser permeability for magnetism, whether
it be an air-gap or an arch of hard steel destined to re-
tain some of its magnetism, you require magneto-motive
force enough to drive the magnetism through that re-
sisting medium; and, therefore, you must have turns of
wire. That implies that you must have length of leg
on which to wind those turns. "Ritchie also found that
the amount of magnetism remaining behind in the soft
iron arch, after turning off the current at the first re-
moval of the armature, was a little greater with long
than with short magnets; and, indeed, it is what we
should expect now, knowing the properties of iron, that
long pieces, however soft, retain a little more have a
little more memory, as it were, of having been magnet-
ized than short pieces. Later on I shall have specially
to draw your attention to the behavior of short pieces of
iron which have no magnetic memory.

LECTURES ON THE ELECTROMAGNET. 173

WINDING OF THE COPPER.

I now take up the question of winding the copper
wire upon the electromagnet. How are we to determine
beforehand the amount of wire required and the proper
gauge of wire to employ ?

The first stage of such a determination is already ac-
complished; we are already in possession of the formula
for reckoning out the number of ampere turns of ex-
citation required in any given case. It remains to show
how from this to calculate the amount of bobbin space,
and the quantity of wire to fill it. Bear in mind that a
current of 10 amperes (i. e., as strong as that used for a
big arc light) flowing once around the iron produces
exactly the same effect magnetically as a current of one
ampere flowing around ten times, or as a current of
only one-hundredth part of an ampere flowing around
a thousand times. In telegraphic work the currents
ordinarily used in the lines are quite small, usually
from five to twenty thousandths of an ampere; hence
in such cases the wire that is wound on need only be a
thin one, but it must have a great many turns. Be-
cause it is thin and has a great many turns, and is con-
sequently a long wire, it will offer a considerable resist-
ance. That is no advantage, but does not necessarily
imply any greater waste of energy than if a thicker coil
of fewer turns were used with a correspondingly larger
current. Consider a very simple case. Suppose a bob-
bin is already filled with a certain number of turns of
wire, say 100, of a size large enough to carry one ampere,
without overheating. It will offer a certain resistance,

174 LECTURES ON THE ELECTROMAGNET.

it will waste a certain amount of the energy of the cur-
rent, and it will have a certain magnetizing power.
Now suppose this -bobbin to be rewound with a wire of
half the diameter; what will the result be ? If the
wire is half the diameter it will have one-quarter the
sectional area, and the bobbin will hold four times as
many turns (assuming insulating materials to occupy
the same percentage of the available volume). The cur-
rent which such a wire will carry will be one-fourth as
great. The coil will offer sixteen times as much resist-
ance, being four times as long and of one-fourth the
cross-section of the other wire. But the waste of energy
will be the same, being proportional to the resistance
and to the square of the current: for 16 X T V = 1.
Consequently the heating effect will be the same. Also
the magnetizing power will be the same, for though the
current is only one-quarter of an ampere, it flows
around 400 turns ; the ampere turns are 100, the same
as before. The same argument would hold good with
any other numerical instance that might be given. It
therefore does not matter in the least to the magnetic
behavior of the electromagnet whether it is wound with
thick wire or thin wire, provided the thickness of the
wire corresponds to the current it has to carry, so that
the same number of watts of power are spent in heating
it. For a coil wound on a bobbin of given volume the
magnetizing power is the same for the same heat waste.
But the heat waste increases in a greater ratio than the
magnetizing power, if the current in a given coil is in-
creased; for the heat is proportional to the square of
the current, and the magnetizing power is simply pro-

LECTURES ON THE ELECTROMAGNET. 175

portional to the current. Hence it is the heating effect
which in reality determines the winding of the wire.
We muse assuming that the current will have a certain
strength allow enough volume to admit of our getting
the requisite number of ampere turns without over-
heating. A good way is to assume a current of one
ampere while one calculates out the coil. Having done
this, the same volume holds good for any other gauge
of wire appropriate to any other current. The terms
"long coil" magnet and "short coil" magnet are ap-
propriate for those electromagnets which have, re-
spectively, many turns of thin wire and few turns
of thick wire. These terms are preferable to " high
resistance" and "low resistance," sometimes used to
designate the two classes of windings; because, as I
have just shown, the resistance of a coil has in itself
nothing to do with its magnetizing power. Given the
volume occupied by the copper, then for any current
density (say, for example, a current density of 2,000
amperes per square inch of cross-section of the copper),
the magnetizing power of the coil will be the same for
all different gauges of wire. The specific conductivity
of the copper itself is of importance; for the better the
conductivity the less the heat waste per cubic inch of
winding. High conductivity copper is therefore to be
preferred in every case.

Now the heat which is thus generated by the current
of electricity raises the temperature of the coil (and of
the core), and it begins to emit heat from its surface.
It may be taken as a sufficient approximation that a
single square inch of surface, warmed one degree Fahr,

176 LECTURES ON THE ELECTROMAGNET.

above the surrounding air, will steadily emit heat at the
rate of -g^- of a watt. Or, if there is provided only
enough surface to allow of a steady emission of heat at
the rate of one watt l per square inch of surface, the
temperature of that surface will rise to about 225 de-
grees Fahr. above the temperature of the surrounding
air. This number is determined by the average emis-
sivity of such substances as cotton, silk, varnish, and
other materials of which the surfaces of coils are usu-
ally composed.

In the specifications for dynamo machines it is usual
to lay down a condition that the coils shall not heat
more than a certain number of degrees warmer than the
air. With electromagnets it is a safe rule to say that
no electromagnet ought ever to heat up to a tempera-
ture more than 100 degrees Fahr. above the surrounding
air. In many cases it is quite safe to exceed this limit.

The resistance of the insulated copper wire on a bob-
bin may be approximately calculated by the following
rule. If d is the diameter of the naked wire, in mils,
and D is the diameter, in mils, of the wire when covered,
then the resistance per cubic inch of the coil will be:

.. . , 960,700
Ohms per cubic inch =

1 The watt is the unit of rate of expenditure of energy, and is equal to
ten million ergs per second, or to l-746th of a horse power. A current of one
ampere, flowing through a resistance of one ohm, spends energy in heating
at the rate of one watt. One watt is equivalent to 0.24 calories, per second,
of heat. That is to say, the heat developed in one second, by expenditure of
energy at the rate of one watt, would suffice to warm one gramme of water
through 0.24 (Centigrade) degree. As 252 calories are equal to one British
(pound Fahr.) unit of heat, it follows that heat emitted at the rate of one
watt would suffice to warm 3.4 pounds of water one degree Fahr. in one hour ;
or one British unit of heat equals 1,058 watt seconds,

LECTURES ON THE ELECTROMAGNET. 17T

We are therefore able to construct a wire gauge and
ampereage table which will enable us to calculate readily
the degree to which a given coil will warm when tra-
versed by a given current, or conversely what volume of
coil will be needed to provide the requisite circulation
of current without warming beyond any prescribed ex-
cess.

Accordingly, I here give a wire-gauge and ampereage
table which we have been using for some time at the
Finsbury Technical College. It was calculated out
under my instructions by one of the demonstrators of
the college, Mr. Eustace Thomas, to whom I am in-
debted for the great care bestowed upon the calculations

For many purposes, such as for use in telegraphs and
electric bells, smaller wires than any of those mentioned
in the table are required. The table is, in fact, intei: !
for use in calculating .n gnets in larger engineer!,
work.

A rough-and-ready rule sometimes given for the size
of wire is to allow T oVo square inch per ampere. This
is an absurd rule, however, as the figures in the table
show. Under the heading 1,000 amperes to square inch,
it appears tha^ if a No. 18 S. W. G. wire is used it will
at that rate carry 1.81 amperes; that if there is only
one layer of wire, it will only warm up 4.G4 degrees
Fahr., consequently one might wind layer after layer to
a depth of 3.3 inches, without getting up to the limit of
allowing one square inch per watt for the emission of
heat. In very few cases does one want to wind a coil so
thick as 3.3 inches. For very few electromagnets is it
needful that the layer of coil exceed half an inch in
12

178

LECTURES ON THE ELECTROMAGNET.

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LECTURES ON THE ELECTROMAGNET. 179

thickness; and if the layer is going to be only half an
inch thick, or about one-seventh of the 3.3, one may
use a current density A/7 times as great as 1,000 am-
peres per square inch, without exceeding the limit of
safe working. Indeed, with coils only half an inch
thick, one may safely employ a current density of 3,000
amperes per square inch, owing to the assistance which
the core gives for the dissipation and emission of heat.
Suppose, then, we have designed a horseshoe magnet,
with a core one inch in diameter, and that, after con-
sidering the work it has to do, it is found that a mag-
netizing power of 2,400 turns is required; suppose, also,

Figures in columns marked A signify number of amperes that the wire
carries.

Figures in columns marked F signify number of degrees (Fahrenheit)
that the coil will warm up if there is only one layer of w r ire, and on the
assumption that the heat is radiated only from the outer surface of the
coil ; they are calculated by the following modification of Forbes 1 rule :

Rise in temperature (Fahrenheit deg.) = 225 x No. of watts lost per sq. inch.

= 159 x sectional area X number of
turns to one inch (at 1,000 amps,
per sq. inch).

Figures in columns marked D are the depth in inches to which wire may
be wound if one watt be lost by each square inch of radiating surface, the
outside radiating surface of the bobbin being only considered.

Rule for calculating a 7-strand cable: Diatn. of cable = 1.134 X diam. of
equivalent round wire.

Figures under heading "Turns to one linear inch 11 are calculated for
cotton covered wires of average thicknesses of coverings used for the dif-
ferent gauges, viz., 14 mils additional diameter on round wires (from No. 22)
and 20 mils on stranded or square wire.

Figures under heading "Turns per square inch 11 are calculated from
preceding, allowing 10 per cent, for bedding of layers.

Resistance (ohms) of coil of copper wire, occupying v cubic inches of coil
space, and of which the gauge is d mils uncovered, and D mils covered, may
be approximately calculated by the rule :

ohms = 960,700^

The data respecting sizes of wires of various gauges are kindly furnished by
the London Electric Wire Company.

180 LECTURES ON THE ELECTROMAGNET.

that it is laid down as a condition that the coil
must not warm up more than 50 degrees Fahr. above
the surrounding air what volume of coil will be re-
quired ? Assume, first, that the current will be one
ampere; then there will have to be 2,400 turns of a
wire which will carry one ampere. If we took a No.
20 S. W. G. wire and wound it to the depth of half an
inch, that would give 220 turns per inch length of coil;
so that a coil 11 inches long and a little over half an
inch deep (or ten layers deep) would give 2,400 turns.
Now Table X. shows that if this wire were to carry
1.018 amperes it would heat up 225 degrees Fahr. if
wound to a depth of 3.9 inches. If wound to half an
inch, it would therefore heat up about 30 degrees Fahr.;
and with only one ampere would, of course, heat less.
This is too good; try the next thinner wire. No. 22 S.
W. G. wire at 2,000 amperes to the square inch will
carry 1.23 amperes, and heats 225 degrees if wound up
1.13 inches. If it is only to heat 50 degrees, it must
not be wound more than one-fourth inch deep; but if
it only carries current of one ampere it may be wound
a little deeper say to 14 layers. There will then be
wanted a coil about seven inches long to hold the 2,400
turns. The wire will occupy about 3.85 square inches
of total cross-section, and the volume of the space oc-
cupied by the winding will be 26.95 cubic inches. Two
bobbins, each 3| inches long and .65 deep, to allow for
14 layers, will be suitable to receive the coils.

By the light of the knowledge one possesses as to the
relation between emissivity of surface, rate of heating
by current, and limiting temperatures, it is seen how

LECTURES ON THE ELECTROMAGNET 181

little justification there is for such empirical rules cs
that which is often given, namely, to make the depth
of coil equal to the diameter of the iron core. Consider
this in relation to the following fact ; that in all those
cases where leakage is negligible the number of ampere-
turns that will magnetize up a thin core to any pre-
scribed degree of magnetization will magnetize up a
core of any section whatever, and of the same length, to
the same degree of magnetization. A rule that would
increase the depth of copper proportionately to the
diameter of ':he iron core is absurd.

Where less accurate approximations are all that is
needed, more simple rules can be given. Here are two
cases :

Case 1. Lea/cage assumed to be negligible. Assume
B = 16,000, then H = 50 (see Table III.). Hence the
ampere turns per centimetre of iron will have to be 40,
or per inch of iron 102; for H is equal to 1.2566 times
the ampere turns per centimetre. Now, if the winding
is not going to exceed one-half inch in depth, we may
allow 4,000 amperes per square inch without serious
overheating. And the 4,000 ampere turns will require
2-inch length of coil, or each inch of coil carries 2,000
ampere turns without overheating. Hence each inch
of coil one-half inch deep will suffice to magnetize up
20 inches length of iron to the prescribed degree.

Case 2. Leakage assumed to be 50 per cent. Assume
B in air-gap = H = 8,000, then to force this across re-
quires ampere turns 6,400 per centimetre of air, or 16,-
250 per inch of air. Now, if winding is not going to
exceed one-half inch depth, each inch length of coil will

182 LECTURES Otf THE ELECTROMAGNET.

carry 2,000 ampere tu A Hence, eight inches length
of coil one-quarter inch deep will be required for one
inch length of air, magnetized up to the prescribed de-
gree.

WINDINGS FOE CONSTANT PRESSURE AND FOR
CONSTANT CURRENT.

In winding coils for magnets that are to be used on
any electric light system, it should be carefully borne
in mind that there are separate rules to be considered
according to the nature of the supply. If the electric
supply is at constant pressure, as usual for glow lamps,
the winding of coils of electromagnets follows the same
rule as the coils of voltmeters. If the supply is with
constant current, as usual for arc lighting in series, then
the coils must be wound with due regard to the current
which the wire will carry, when lying in layers of suita-
ble thickness, the number of turns being in this case the
same whether thin or thick wire is used.

If we assume that a safe limit of temperature is 90
degrees Fahr. higher than the surrounding air, then the
largest current which may be used with a given electro-
magnet is expressed by the formula:

Highest permissible amperes = 0.63 V -

where s is the number of square inches of surface of
the coils and r their resistance in ohms.

Similarly for coils to be used as shunts we have:

Highest permissible volts = 0.63 V sr

LECTURES ON THE ELECTROMAGNET. 183

The magnetizing power of a coil, supplied at a given
number of volts of pressure, is independent of its length,
and depends only on its gauge, but the longer the wire
the less will be the heat waste. On the contrary, when
the condition of supply is with a constant number of
amperes of current, the magnetizing power of a coil is
independent of the gauge of the wire, and depends only
on its length; but the larger the gauge the less will be
the heat waste.

MISCELLANEOUS RULES ABOUT WINDING.

To reach the same limiting temperature with bobbins
of equal size, wound with wires of different gauge, the
cross-section of the wire must vary with the current it
is to carry; or, in other words, the current density
(amperes per square inch) must be the same in each.
Table X. shows the ampereages of the various sizes of
wires at four different values of current density.

To raise to the same temperature two similarly shaped
coils, differing in size only, and having the gauges of
the wires in the same ratio (so that there are the same
number of turns on the large coil as on the small one),
the currents must be proportional to the square roots of
the cubes of the linear dimensions.

Sir William Thomson has given a useful rule for cal-
culating windings of electromagnets of the same type
but of different sizes. Similar iron cores, similarly
wound with lengths of wire proportional to the squares
of their linear dimensions, will, when excited with equal
currents, produce equal intensities of magnetic field at
points similarly situated with respect to them.

184 LECTURES ON THE ELECTROMAGNET.

Similar electromagnets of different sizes must have
ampere turns proportional to their linear dimensions if
they are to be magnetized up to an equal degree of sat-
uration.

It is curious what erroneous notions crop up from
time to time about winding electromagnets. In 1869
a certain Mr. Lyttle took out a patent for winding the
coils in the following way: Wind the first layer as
usual, then bring the wire back to the end where the
winding began and wind a second layer, and so on. In
this way all the windings will be right-handed, or else
all left-handed, not alternately right and left as in the
ordinary winding. Lyttle declared that this method of
winding a coil gave more powerful effects; so did M.
Brisson, who reinvented the same mode of winding in
1873, and solemnly described it. Its alleged superiority
was at once disproved by Mr. W. H. Preece, who
found the only difference to be that there was more
difficulty in carrying out this mode of winding.

Another popular error is that electromagnets in which
the wires are badly insulated are more powerful than
those in which they are well insulated. This arises
from the ignorant use of electromagnets having long,
thin coils (of high resistance) with batteries consisting
of a few cells (of low electromotive force). In such
cases, if some of the coils are short circuited, more cur-
rent flows, and the magnetizing power may be greater.
But the scientific cure is either to rewind the magnet
with an appropriate coil of thick wire, or else to apply
another battery having an electromotive force that is
greater.

LECTURES ON THE ELECTROMAGNET. 185

SPECIFICATIONS OF ELECTROMAGNETS.

One frequently comes across specifications for con-
struction which prescribe that an electromagnet shall be
wound so that its coil shall have a certain resistance.
This is an absurdity. Eesistance does not help to 'mag-
netize the core. A better way of prescribing the wind-
ing is to name the ampere turns and the temperature
limit of heating. Another way is to prescribe the num-
ber of watts of energy which the magnet is to take.
Indeed, it would be well if electricians could agree upon
some sort of figure of merit by which to compare elec-
tromagnets, which should take into account the magnetic
output L e., the product of magnetic flux into magneto-
motive force the consumption of energy in watts, the
temperature rise, and the like.

AMATEUR RULE ABOUT RESISTANCE OF ELECTRO-
MAGNET AND BATTERY.

In dealing with this question of winding copper on a
magnet core, I cannot desist from referring to that rule
which is so often given, which I often wish might dis-
appear from our text-books the rule which tells you in
effect that you are to waste 50 per cent, of the energy
you employ. I refer to the rule which states that you
will get the maximum effect out of an electromagnet if
you so wind it that the resistance is equal to the resist-
ance of the battery you employ; or that if you have a
magnet of a given resistance you ought to employ a
battery of the same resistance. "What is the meaning of
this rule ? It is a rule which is absolutely meaningless,

186 LECTURES ON THE ELECTROMAGNET.

unless in the first case the volume of the coil is pre-
scribed once for all, and you cannot alter it; or unless
once for all the number of battery elements that you
can have is prescribed. If you have to deal with a fixed
number of battery elements, and you have to get out
of them the biggest effect in your external circuit, and
cannot beg, buy, or borrow any more cells, it is per-
fectly true that, for steady currents, you ought to group
them so that their internal resistance is equal to the
external resistance that they have to work through; and
then, as a matter of fact, half the energy of the battery
will be wasted, but the output will be a maximum. Now
that is a very nice rule indeed for amateurs, because an
amateur generally starts with the notion that he does
not want to economize in his rate of working; it does
not matter whether the battery is working away furi-
ously, heating itself, and wasting a lot of power; all he
wants is to have the biggest possible effect for a little
time out of the fewest cells. It is purely an amateur's
rule, therefore, about equating the resistance inside to
the resistance outside. But it is absolutely fallacious to
set up any such rule for serious working; and not only
fallacious, but absolutely untrue if you are going to deal
with currents that are going to be turned off and on
quickly. For any apparatus like an electric bell, or
rapid telegraph, or induction coil, or any of those
things where the current is going to vary up and down
rapidly, it is a false rule, as we shall see presently.
What is the real point of view from which one ought to
start ? I am often asked questions by, shall I say, ama-
teurs, as well as by those who are not amateurs, about

LECTURES ON THE ELECTROMAGNET. 187

prescribing the battery for a given electromagnet, or
prescribing an electromagnet for a given battery. Again,
I am often told of cases of failure, in which a very little
common sense rightly directed might have made a suc-
cess. What one ought to think about in every case is
not the battery, not the electromagnet, but the line.
If you have a line, then you must have a battery and
electromagnet to correspond. If the line is short and
thick, a few feet of good copper wire, you should have
a short, thick battery, a few big cells or one big cell, and
a short, thick coil on your electromagnet. If you have
a long, thin line, miles of ft, say, you want a long, thin
battery (small cells, and a long row of them) and a long,
thin coil. That is then our rule : for a short, thick line,
a short, thick battery and a short, thick coil; for a long,
thin line, a long, thin battery and electromagnet coils
to match. You smile; but it is a really good rule that
I am giving you; vastly better than the worn-out ama-
teur rule.

But, after all, my rule does not settle the whole ques-
tion, because there is something more than the whole
resistance of the circuit to be taken into account.
Whenever you come to rapidly acting apparatus, you
have to think of the fact that the current, while vary-
ing, is governed not so much by the resistance as by
the inertia of the circuit its electromagnetic inertia.
As this is a matter which will claim our especial atten-
tion hereafter, I will leave battery rules for the present
and proceed with the question of design.

188 LECTURES ON THE ELECTROMAGNET.

FORMS OF ELECTROMAGNETS.

This at once leads us to consider the classification of
forms of magnets. I do not pretend to have found a
complete classification. There is a very singular book
written by Monsieur Nickles, in which he classifies under
37 different heads all conceivable kinds of magnets,
bidromic, tridromic, monocnemic, multidromic, and I
do not know how many more; but the classification is
both unmeaning and unmanageable. For my present
purpose I will simply pick out those which come under
three or four heads, and deal separately with others that
do not quite fit under any of the four categories.

Bar Electromagnets. In the first place there are those
which have a straight core, of which there are several
specimens on the table here.

Horseshoe Electromagnets. Then there are the horse-
shoes, of which some are of one piece, bent, and others
here of the more frequent shape, made of three pieces.

Iron-clad Electromagnets. Then from the horseshoes
I go to those magnets in which the return circuit of the
iron comes back outside the coil from one end or the
other, or from both ends, sometimes in the form of an
external tube or jacket, sometimes merely with a parallel
return yoke, or two parallel return yokes. All such
magnets I propose to call following the fashion that
has been adopted for dynamos iron-clad electromagnets.
One of them, the jacketed electromagnet, is shown in
Fig. 12, and there are others not so well known. There
is one used by Mr. Cromwell Varley, in which a straight
magnet is placed between a couple of iron caps, which

LECTURES ON THE ELECTROMAGNET. 189

fit over the ends, and virtually bring the poles down
close together, the circular rim of one cap being the
north pole and that of the other cap being the south
pole, the two rims being close together. That plan, of
course, produces a great tendency to leak across from
one rim to the other all round. The advantages, as
well as the disadvantages, of the jacketed magnet I
alluded to in my last lecture, when I pointed out to you
that for all action at a distance it is far better not to
have an iron-clad return
path, whereas for action in
contact the iron-clad magnet
was distinctly a very good
form. In one form of iron-
clad magnet the end of the
straight central core is fixed
to the middle of a bar of ^ ^ 1 i- 1

iron, the ends Of which are FIG. 50.- CLUB-FOOTED ELECTRO-

bent up and brought flush

with the top of the bobbin, making thus a tripolar
magnet, with one pole between the other two. The
armature in this form is a bar which lies right across
the three poles. There is an example of this excellent
kind of electromagnet applied in one of the forms of
electric bell indicator made by Messrs. Gent, of Leicester.
Then besides these three main classes the straight
bar, the horseshoe, and the iron-clad there is another
form which is so useful and so commonly employed in
certain work that it deserves to have a name of its own.
It is that called by Count Du Moncel iheaimant boiteux,
or club-footed magnet (Fig. 50). It is a horseshoe, in

190 LECTURES ON THE ELECTROMAGNET.

fact, with a coil upon one pole and no coil upon the
other. The advantage of that construction is simply, I
suppose, that you will save labor you will only have to
wind the wire on one pole instead of two. Whether
that is an improvement in any other sense is a question
for experiment to determine, but on which theory per-
haps might now be able to say something. Count Du
Moncel, who made many experiments on this form of
magnet, ascertained that there was for an equal weight
of copper a slight falling off in power with the club-
footed magnet. Indeed, one might almost predict, for
a given weight of copper, if you wound all in one coil
only, you will not make as many turns as if you wound
it in two, the outer turns on the coil being so much
larger than the average turn when wound in two coils.
Consequently the number of ampere turns with a given
weight of copper would be rather smaller, and you would
require more current to bring the magnetizing power
up to the same value as with the two coils. At the same
time the one coil may be produced a little more cheaply
than the two; and indeed such electromagnets are really
quite common, being largely used for the sake of cheap-
ness and compactness in indicators or electric bells.

Du Moncel tried various experiments about this form
to find whether it acted better when the armature was
pivoted over one pole or over the other, and found it
worked best when the armature was actually hinged on
to that pole which comes up through the coil. He made
two experiments, trying coils on one or the other limb,
the armature being in each case set at an equal distance.
In one experiment he found the pull was 35 grammes,

LECTURES ON THE ELECTROMAGNET. 191

with an armature hinged on to the idle pole, and 40
grammes when it was hinged on to the pole which car-
ried the coil.

Another form of electromagnet, having but one coil,
is used in the electric bells of church-bell pattern, of
which Mr. H. Jensen is the designer. In Jensen's elec-
tromagnet a straight cylindrical core receives the bob-
bin for the coil, and, after this has been pushed into its
place, two ovate pole-pieces are screwed upon its ends,
serving thus to bring the magnetic circuit across the
ends of the bobbin, and forming a magnetic gap along
the side of the bobbin. The armature is a rectangular
strip of soft iron, about the same length as the core, and
is attracted at one end by one pole-piece and at the
other end by the other.

EFFECT OF SIZE OF COILS.

Seeing that the magnetizing power which a coil ex-
erts on the magnetic circuit which it surrounds is sim-
ply proportional to the ampere turns, it follows that
those turns which lie on the outside layers of the coil,
though they are further away from the iron core, pos-
sess precisely equal magnetizing power. This is strictly
true for all closed magnetic circuits; but in those open
magnetic circuits where leakage occurs it is only true
for those coils which encircle the leakage lines also. For
example, in a short bar electromagnet, of the wide
turns on the outer layer, those which encircle the mid-
dle part of the bar do inclose all the magnetic lines, and
are just as operative as the smaller turns that underlie
them ; while those wide turns which encircle the end

192 LECTUHES ON THE ELECTROMAGNET.

portions of the bur are not so efficient, as some of the
magnetic lines leak back past these coils.

EFFECT OF POSITION OF COILS.

Among the other researches which Du Moncel made
with respect to electromagnets was one on the best posi-
tion for placing the coil upon the iron core. This is a
matter that other experimenters have examined. In
Dub's book, "Elektromagnetismus," to which I have
several times referred, you will also find many experi-
ments on the best position of a coil; but it is perhaps
sufficient to narrate a single example. Du Moncel had
four pairs of bobbins made of exactly the same volume,
and with 50 metres of wire on each ; one pair was 16
centimetres long, another pair eight centimetres, or half
the length, with not quite so many turns, because of
course the diameter of the outer turn was larger, one
four centimetres in length and another two centime-
tres. These were tried both with bar magnets and
horseshoes. It will suffice, perhaps, to give the result
of the horseshoe. The horseshoe was made long enough
16 centimetres only, a little over six inches long to
carry the longest coil. Now when the compact coils
two centimetres long were used, the pull on the arma-
ture at a distance away of two millimetres (it was al-
ways the same, of course, in the experiments) was 40
grammes. Using the same weight of wire, but distrib-
uted on the coils twice as long, the pull was 55 grammes.
Using the coils eight centimetres long it was 75 grammes,
and using the coils 16 centimetres long, covering the
length of each limb, the pull was 85, clearly showing

LECTURES ON THE ELECTROMAGNET. 193

that, where you have a given length of iron, the best
way of winding a magnet to make it pull with its great-
est pull is not to heap the coil up against the poles, but
to wind it uniformly; for this mode of winding will give
you more turns, therefore more ampere turns, therefore
more magnetization. An exception might, however,
occur in some case where there is a large percentage of
leakage. With club-footed magnets results of the same
kind are obtained. It was found in every case that it
was well to distribute the coil as much as possible along
the length of the limb. All these experiments were
made with a steady current. It does not follow, how-
ever, because winding the wire over the whole length of
core is best for steady currents that it is the best wind-
ing in the case of a rapidly varying current; indeed, we
shall see that it is not.

EFFECT OF SHAPE OF SECTION.

So far as the carrying capacity for magnetic lines is
concerned, one shape of section of cores is as good as
another; square or rectangular is as good as round if
containing equal sectional area. But there are two
other reasons, both of which tell in favor of round cores.
First, the leakage of magnetic lines from core to core is,
for equal mean distances apart, proportional to the sur-
face of the core; and the round core has less surface
than square or rectangular of equal section. All edges
and corners, moreover, promote leakage. Secondly, the
quantity of copper wire that is required for each turn
will be less for round cores than for cores any other

194 LECTURES ON THE ELECTROMAGNET.

shape, for of all geometrical figures of equal area the
circle is the one of the least periphery.

EFFECT OF DISTANCE BETWEEN POLES,

Another matter that Du Moncel experimented upon,
and Dub and Nickles likewise, was the distance between
the poles. Dub considered that it made no difference
how far the poles were apart. Nickles had a special ar-
rangement made which permitted him to move the two
upright cores or limbs, nine centimetres high, to and
fro on a solid bench or yoke of iron. His armature was
30 centimetres long. Using very weak currents, he
found the effect best when the shortest distance be-
tween the poles was three centimetres; with a stronger
current, 12 centimetres; and with his strongest current,
nearly 30 centimetres. I think leakage must have a
deal to do with these results. Du Moncel tried various
experiments to elucidate this matter, and so did Prof.
Hughes in an important but too little known re-
search, which came out in the Annales Telegraphiques
in the year 1862.

KESEARCHES OF PEOFESSOE HUGHES.

His object was to find out the best form of electro-
magnet, the best distance between the poles, and the
best form of armature for the rapid work required in
Hughes' printing telegraphs. One word about Hughes'
magnet. This diagram (Fig. 51) shows the form of
the well known Hughes electromagnet. 1 feel almost
ashamed to say those words "well known," because al-
though on the Continent everybody knows what you

LECTURES ON THE ELECTROMAGNET.

195

mean by a Hughes electromagnet, in England scarcely
any one knows what you mean. Englishmen do not
even know that Prof. Hughes has invented a special
form of electromagnet. Hughes' special form is this :
A permanent steel magnet, generally a compound one,
having soft iron pole-pieces, and a couple of coils on the
pole-pieces only. As I have to speak of Hughes' spe-
cial contrivance among the mechanisms that will oc-

FIG. 51. HUGHES' ELECTROMAGNET.

cupy our attention next week, I only now refer to this
magnet in one particular. If you wish a magnet to
work rapidly, you will secure the most rapid action, not
when the coils are distributed all along, but when they
are heaped up near, not necessarily entirely on, the
poles. Hughes made a number of researches to find out
what the right length and thickness of these pole-pieces
should be. It was found an advantage not to use too
thin pole-pieces, otherwise the magnetism from the per-

196 LECTURES ON THE ELECTROMAGNET.

manent magnet did not pass through the iron without
considerable reluctance, being choked by insufficiency
of section; also not to use too thick pieces, otherwise
they presented too much surface for leakage across from
one to the other. Eventually a particular length was
settled upon, in proportion about six times the diame-
ter, or rather longer. In the further researches that
Hughes made he used a magnet of shorter form, not
shown here, more like those employed in relays, and
with an armature from two to three millimetres thick,
one centimetre wide, and five centimetres long. The
poles were turned over at the top toward one another.
Hughes tried whether there was any advantage
in making those poles approach one another, and
whether there was any advantage in having as long an
armature as five centimetres. He tried all different
kinds, and plotted out the results of observations in
curves, which could be compared and studied. His ob-
ject was to ascertain the conditions which would give
the strongest pull, not with a steady current, but with
such currents as were required for operating his print-
ing telegraph instruments ; currents which lasted only
from one to twenty hundredths of a second. He found
it was decidedly an advantage to shorten the length of
the armature, so that it did not protrude far over the
poles. In fact, he got a sufficient magnetic circuit to
secure all the attractive power that he needed, without
allowing as much chance of leakage as there would have
been had the armature extended a longer distance over
the poles. He also tried various forms of armature
having very various cross-sections,

LECTURES ON THE ELECTROMAGNET. 197

POSITION AND FORM OF ARMATURE.

In one of Du MonceFs papers on electromagnets 2 you
will also find a discussion on armatures, and the best
forms for working in different positions. Among
other things in Du Moncel you will find this paradox ;
that whereas, using a horseshoe magnet with flat poles,
and a flat piece of soft iron for armature, it sticks on
far tighter when put on edgewise, on the other hand,
if you are going to work at a distance, across air, the
attraction is far greater when it is set flatwise. I
explained the advantage of narrowing the surfaces of
contact by the law of traction, B 2 coming in. Why
should we have for an action at a distance the greater
advantage from placing the armature flatwise to the
poles? It is simply that you thereby reduce the reluc-\ f\ J^\
tance offered by the air-gap to the flow of the magnetic '
lines. Du Moncel also tried the difference between ) fj/'
round armatures and flat ones, and found that a cylin-
drical armature was only attracted about half as strongly $**
as a prismatic armature having the same surface when
at the same distance. Let us examine this fact in the
light of the magnetic circuit. The poles are flat. You
have at a certain distance away a round armature ; there
is a certain distance between its nearest side and the
polar surfaces. If you have at the same distance away
a flat armature having the same surface, and, therefore,
about the same tendency to leak, why do you get a
greater pull in this case than in that ? I think it is
clear that, if they are at the same distance away, giving

2 La Lumiere Electrique, vol. ii.

198 LECTURES ON THE ELECTROMAGNET.

the same range of motion, there is a greater magnetic
reluctance in the case of the round armature, although
there is the same periphery, because though the nearest
part of the surface is at the prescribed distance, the rest
of the under surface is farther away, so that the gain
found in substituting an armature with a flat surface is
a gain resulting from the diminution in the resistance
offered by the air-gap.

POLE-PIECES ON HORSESHOE MAGNETS,

Another of Du Moncel's researches 3 relates to the
effect of polar projections or shoes movable pole-pieces,
if you like upon a horseshoe electromagnet. The core
of this magnet was of round iron four centimetres in
diameter, and the parallel limbs were ten centimetres
long and six centimetres apart. The shoes consisted of
two flat pieces of iron slotted out at one end, so that
they could be slid along over the poles and brought
nearer together. The attraction exerted on a flat arma-
ture across air-gaps two millimetres thick was measured
by counterpoising. Exciting this electromagnet with a
certain battery, it was found that the attraction was
greatest when the shoes were pushed to about 15 milli-
metres, or about one-quarter of the inter-polar distance,
apart. The numbers were as follows:

Distance between

shoes. Attraction,

Millimetres. in grammes.

2 900

10 1,012

15 1,025

25 965

40 890

60 550

_ _i_ . . . . .

8 La Lumiere Electrique, vol. iv., p. 129.

LECTURES ON THE ELECTROMAGNET. 199

With, a stronger battery the magnet without shoes
had an attraction of 885 grammes, but with the shoes 15
millimetres apart, 1,195 grammes. When one pole only
was employed, the attraction, which was 88 grammes
without a shoe, was diminished by adding a shoe to 39
grammes !

CONTRAST BETWEEN ELECTROMAGNETS AND PER-
MANENT MAGNETS.

Now, I want particularly to ask you to guard against
the idea that all these results obtained from electro-
magnets are equally applicable to permanent magnets
of steel; they are not, for this simple reason. With
an electromagnet, when you put the armature near, and
make the magnetic circuit better, you not only get more
magnetic lines going through that armature, but you
get more magnetic lines going through the whole of the
iron. You get more magnetic lines round the bend
when you put an armature on to the poles, because you
have a magnetic circuit of less reluctance, with the same
external magnetizing power in the coils acting around
it. Therefore, in that case, you will have a greater mag-
netic flux all the way round. The data obtained with
the electromagnet (Fig. 43), with the exploring coil C
on the bend of the core, when the armature was in con-
tact and when it was removed, are most significant.
When the armature was present it multiplied the total
magnetic flow tenfold for weak currents and nearly
threefold for strong currents. But with a steel horse-
shoe, magnetized once for all, the magnetic lines that
flow around the bend of the steel are a fixed quantity,

&*

200 LECTURES ON THE ELECTROMAGNET.

and, however much you diminish the reluctance of the
magnetic circuit, you do not create or evoke any more.
When the armature is away the magnetic lines arch
across, not at the ends of the horseshoe only, but from
its flanks, the whole of the magnetic lines leaking some-
how across the space. When you have put the armature
x- on, these lines, instead of
arching out into space as
freely as they did, pass for
the most part along the steel
limbs and through the iron arma-
ture*. You may still have a con-
siderable amount of leakage, but
you have not made one line more go
through the bent part. You have
absolutely the same number going
through the bend with the arma-
ture off as with the armature on.
You do not add to the total num-
ber by reducing the magnetic re-
luctance, because you are not work-

FIG.52.-EXPERIMENTWITH ^ *i nnuence O f a

PERMANENT MAGNET.

constantly impressed magnetizing
force. By putting the armature on to a steel horseshoe
magnet you only colled the magnetic lines, you do not
multiply them. This is not a matter of conjecture.
A group of my students have been making experiments
in the following way : They took this large steel horse-
shoe magnet (Fig. 52), the length of which from end to
end through the steel is 42^ inches. A light narrow
frame was constructed, so that it could be slipped on

LECTURES ON THE ELECTROMAGNET. 201

over the magnet, and on it were wound 30 turns of fine
wire, to serve as an exploring coil. The ends of this
coil were carried to a distant part of the laboratory, and
connected to a sensitive ballistic galvanometer. The
mode of experimenting is as follows : The coil is slipped
on over the magnet (or over its armature) to any desired
position. The armature of the magnet is placed gently
upon the poles, and time enough is allowed to elapse
for the galvanometer needle to settle to zero. The
armature is then suddenly detached. The first SAving
measures the change, due to removing the armature, in
the number of magnetic lines that pass through the
coil in the particular position.

I will roughly repeat the experiment before you; the
spot of light on the screen is reflected from my galva-
nometer at the far end of the table. I place the explor-
ing coil just over the pole, and slide on the armature ;
then close the galvanometer circuit. Now I detach the
armature, and you observe the large swing. I shift the
exploring coil, right up to the bend; replace the arma-
ture; wait until the spot of light is brought to rest at
the zero of the scale. Now, on detaching the armature,
the movement of the spot of light is quite impercepti-
ble. In our careful laboratory experiments the effect
was noticed inch by inch all along the magnet. The
effect when the exploring coil was over the bend was
not as great as l-3000th part of the effect when the coil
.was hard up to the pole. We are therefore justified in
saying that the number of magnetic lines in a perma-
nently magnetized steel horseshoe magnet is not altered
by the presence or absence of the armature.

202 LECTURES ON THE ELECTROMAGNET.

You will have noticed that I always put on the arma-
ture gently. It does not do to slam on the armature ;
every time you do so you knock some of the so-called
permanent magnetism out of it. But you may pull off
the armature as suddenly as you like. It does the mag-
net good rather than harm. There is a popular super-
stition that you ought never to pull off the keeper of a
magnet suddenly. On investigation, it is found that
the facts are just the other way. You may pull off the
keeper as suddenly as you like; but you should never
slam it on.

From these experimental results I pass to the special
design of electromagnets for special purposes.

ELECTROMAGNETS FOB MAXIMUM TRACTION.

These have already been dealt with in the preceding
lecture, the characteristic feature of all the forms suit-
able for traction being the compact magnetic circuit.

Several times it has been proposed to increase the
power of electromagnets by constructing them with in-
termediate masses of iron between the central core and
the outside, between the layers of windings. All these
constructions are founded on fallacies. Such iron is far
better placed either right inside the coils or right out-
side them, so that it may properly constitute a part of
the magnetic circuit. The constructions known as
Oamacho's and Cancels, and one patented by Mr. S. A.
Varley in 1877, belonging to this delusive order of ideas,
are now entirely obsolete.

Another construction which is periodically brought
forward as a novelty is the use of iron windings of wire

LECTURES ON THE ELECTROMAGNET. 203

or strip in place of copper winding. The lower elec-
tric conductivity of iron, as compared with copper,
makes such a construction wasteful of exciting power.
To apply equal magnetizing power by means of an iron
coil implies the expenditure of about six times as many
watts as need be expended if the coil is of copper.

ELECTROMAGNETS FOR MAXIMUM RANGE OF
ATTRACTION.

We have already laid down the principle which will
enable us to design electromagnets to act at a distance.
We want our magnet to project, as it were, its force
across the greatest length of air-gap. Clearly, then,
such a magnet must have a very large magnetizing
power, with many ampere turns upon it, to be able to
make the required number of magnetic lines pass across
the air resistance. Also it is clear that the poles must
not be too close together for its work, otherwise the
magnetic lines at one pole will be likely to coil round
and take short cuts to the other pole. There must be a
wider width between the poles than is desirable in elec-
tromagnets for traction.

ELECTROMAGNETS OF MINIMUM WEIGHT.

In designing an apparatus to put on board a boat or
a balloon, where weight is a consideration of primary
importance, there is again a difference. There are three
things that come into play iron, copper, and electric
current. The current weighs nothing; therefore if you
are going to sacrifice everything else to weight, you may
have comparatively little iron; but you must have

04 LECTURES ON THE ELECTROMAGNET.

enough copper to be able to carry the electric current;
and under such circumstances you must not mind heat-
ing your wires nearly red hot to pass the biggest possi-
ble current. Provide as little copper as you conveniently
can, sacrificing economy in that case to the attainment
of your object; but, of course, you must use fire-proof
material, such as asbestos, for insulating, instead of cot-
ton or silk.

A USEFUL GUIDING PRINCIPLE.

In all cases of design there is one leading principle
which will be found of great assistance; namely, that a
magnet always tends so to act as though it tried to
diminish the length of its magnetic circuit. It tries to
grow more compact. This is the reverse of that which
holds good with an electric current. The electric cir-
cuit always tries to enlarge itself, so as to inclose as
much space as possible, but the magnetic circuit always
tries to make itself as compact as possible. Armatures
are drawn in as near as can be, to close up the magnetic
circuit. Many two-pole electromagnets show a tendency
to bend together when the current is turned on. One
form in particular, which was devised by Ruhmkorff for
the purpose of repeating Faraday's celebrated experi-
ment on the magnetic rotation of polarized light, is
liable to this defect. Indeed, this form of electromag-
net is often designed very badly, the yoke being too
thin, both mechanically and magnetically, for the pur-
pose which it has to fulfill.

Here is a small electric bell, constructed by Wagener,
of Wiesbaden, the construction of which illustrates this

LECTURES ON THE ELECTROMAGNET. . 205

principle. The electromagnet, a horseshoe,, lies horizon-
tally; its poles are provided with protruding, curved
pins of brass. Through the armature are drilled two
holes, so that it can be hung upon the two brass pins,
and when so hung up it touches the ends of the iron
cores just at one edge, being held from more perfect
contact by a spring. There is no complete gap, there-
fore, in the magnetic circuit. When the current comes
and applies a magnetizing power it finds the magnetic

FIG. 53. ELECTROMAGNETIC POP-GUN.

circuit already complete in the sense that there are no
absolute gaps. But the circuit can be bettered by tilt-
ing the armature to bring it flat against the polar ends,
that being indeed the mode of motion. This is a most
reliable and sensitive pattern of bell.

Electromagnetic Pop-Gun. Here is another curious
illustration of the tendency to complete the magnetic
circuit. Here is a tubular electromagnet (Fig. 53), con-
sisting of a small bobbin, the core of which is an iron
tube about two inches loDg. There is nothing very un-

206 LECTURES ON THE ELECTROMAGNET.

usual about it; it will stick on, as you see, to pieces of
iron when the current is turned on. It clearly is an
ordinary electromagnet in that respect. Now, suppose
I take a little round rod of iron, about an inch long, and
put it into the end of the tube, what will happen when
I turn on my current ? In this apparatus as it stands
the magnetic circuit consists of a short length of iron,
and then all the rest is air. The magnetic circuit will
try to complete itself, not by shortening the iron, but
by lengthening it; by pushing the piece of iron out so
as to afford more surface for leakage. That is exactly
what happens; for, as you see, when I turn on the cur-
rent the little piece of iron shoots out and drops down.
You see that little piece of iron shoot out with consid-
erable force. It becomes a sort of magnetic pop-gun.
This is an experiment which has been twice discovered.
I found it first described by Count Du Moncel, in the
pages of La Lumiere Electrique, under the name of the
"pistolet electromagnetique;" and Mr. Shelf ord Bid-
well invented it independently. I am indebted to him
for the use of this apparatus. He gave an account of it
to the Physical Society in 1885, but the reporter missed
it, I suppose, as there is no record in the society's pro-
ceedings.

ELECTROMAGNETS FOR USE WITH ALTERNATING
CURRENTS.

When you are designing electromagnets for use with
alternating currents, it is necessary to make a change
in one respect, namely, you must so laminate the iron
that internal eddy currents shall not occur; indeed, for

LECTURES ON THE ELECTROMAGNET. 207

all rapid acting electromagnetic apparatus it is a good
rule that the iron must not be solid. It is not usual
with telegraphic instruments to laminate them by mak-
ing up the core of bundles of iron plates or wires, but
they are often made with tubular cores ; that is to say,
the cylindrical iron core is drilled with a hole down the
middle, and the tube so formed is slit with a saw-cut to
prevent the circulation of currents in the substance of
the tube. Now, when electromagnets are to be employed
with rapidly alternating currents, such as are used for
electric lighting, the frequency of the alternations being
usually about 100 periods per second, slitting the cores
is insufficient to guard against eddy currents; nothing
short of completely laminating the cores is a satisfac-
tory remedy. I have here, thanks to the Brush Electric
Engineering Company, an electromagnet of the special
form that is used in the Brush arc lamp when required
for the purpose of working in an alternating current
circuit. It has two bobbins that are screwed up against
the top of an iron box at the head of the lamp. The
iron slab serves as a kind of yoke to carry the magnet-
ism across the top. There are no fixed cores in the
bobbins, which are entered by the ends of a pair of
yoked plungers. Now in the ordinary Brush lamp for
use with a steady current the plungers are simply two
round pieces of iron tapped into a common yoke ; but
for alternate current working this construction must
not be used, and instead a U-shaped double -plunger is
used, made up of laminated iron, riveted together. Of
course it is no novelty to use a laminated core; that de-
vice, first useJ. by Joule, and then by Cowper, has been

208 LECTURES ON THE ELECTROMAGNET.

repatented rather too often during the past 50 years to
be considered as a recent invention.

The alternate rapid reversals of the magnetism in the
magnetic field of an electromagnet, when excited by
alternating electric currents, sets up eddy currents in
every piece of undivided metal within range. All
frames, bobbin tubes, bobbin ends and the like must be
most carefully slit, otherwise they will overheat. If a
domestic flat-iron is placed on the top of the poles of a
properly laminated electromagnet, supplied with alter-
nating' currents, the flat-iron is speedily heated up by
the eddy currents that are generated internally within
it. The eddy currents set up by induction in neighbor-
ing masses of metal, especially in good conducting
metals, such as copper, give rise to many curious phe-
nomena. For example, a copper disc or copper ring
placed over the pole of a straight electromagnet so ex-
cited is violently repelled. These remarkable phenom-
ena have been recently investigated by Prof. Elihu
Thomson, with whose beautiful and elaborate researches
we have lately been made conversant in the pages of the
technical journals. He rightly attributes many of the
repulsion phenomena to the lag in phase of the alternat-
ing currents thus induced in the conducting metal. The
electromagnetic inertia, or self-inductive property of
the electric circuit, causes the currents to rise and fall
later in time than the electromotive forces by which
they are occasioned. In all such cases the impedance
which the circuit offers is made up of two things re-
sistance and inductance. Both these causes tend to
diminish the amount of current that flows, and the in-
ductance also tends to delay the flow,

LECTURES ON THE ELECTROMAGNET. 209

ELECTROMAGNETS FOR QUICKEST ACTION.

I have already mentioned Hughes' researches on the
form of electromagnet best adapted for rapid signaling.
I have also incidentally mentioned the fact that where
rapidly varying currents are employed, the strength of
the electric current that a given battery can yield is de-
termined not so much by the resistance of the electric
circuit, but by its electric inertia. It is not a very easy
task to explain precisely what happens to an electric
circuit when the current is turned on suddenly. The
current does not suddenly rise to its full value, being
retarded by inertia. The ordinary law of Ohm in its
simple form no longer applies; one needs to apply that
other law which bears the name of the law of Helm-
holtz, the use of which is to give us an expression, not
for the final value of the current, but for its value at
any short time, t, after the current has been turned on.
The strength of the current after a lapse of a short time,
t, cannot be calculated by the simple process of taking
the electromotive force and dividing it by the resistance,
as you would calculate steady currents.

In symbols, Helmholtz's law is :

--t\

- e L )

In this formula i t means the strength of the current
after the lapse of a short time t; E is the electromotive
force; R the resistance of the whole circuit; L its co-
efficient of self-induction; arid e the number 2,7183,

210

LECTURES ON THE ELECTROMAGNET.

which is the base of the Napierian logarithms. Let us
look at this formula; in its general form it resembles
Ohm's law, but with a new factor, namely, the expres-
sion contained within the brackets. This factor is nec-
essarily a fractional quantity, for it consists of unity
less a certain negative exponential, which we will pres-
ently further consider. If the factor within brackets is
a quantity less than unity, that signifies that i t will be
less than E -j- R. Now the exponential of negative
sign, and with negative fractional index, is rather a
troublesome thing to deal with in a popular lecture.
Our best way is to calculate some values, and then plot
it out as a curve. When once you have got it into the
form of a curve, you can begin to think about it, for
the curve gives you a mental picture of the facts that
the long formula expresses in the abstract. Accordingly
we will take the following case: Let E = 10 volts; R =
I ohm; and let us take a relatively large self-induction,
so as to exaggerate the effect; say let L = 10 quads.
This gives us the following:

t(sec)

,**

it

1

1
1.105

0.950

2

1.221

1.810

5

1.649

3.936

10

2.718

6.343

20

7.389

8.646

30

20.08

9.501

60

403.4

9.975

120

162800.0

9.999

In this case the value of the steady current as calcu-

LECTURES ON THE ELECTROMAGNET.

211

lated by Ohm's law is 10 amperes; but Helmholtz's
law shows us that with the great self-induction, which
we have assumed to be present, the current, even at the
end of 30 seconds, has only risen up to within 95 per
cent, of its final value; and only at the end of two min-
utes has practically attained full strength. These values
are set out in the highest curve in Fig. 54, in which,
however, the further supposition is made that the num-
ber of spirals S in the coils of the electromagnet is 100,
so that when the current attains its full value of 10

10 20 40 60 80 100 120

FIG. 54. CURVES OF RISE OF CURRENTS.

amperes the full magnetizing power will be Si =
1,000. It will be noticed that the curve rises from zero
at first steeply and nearly in a straight line, then bends
over, and then becomes nearly straight again as it grad-
ually rises to its limiting value. The first part of the
curve that relating to the strength of the current after
a very small interval of time is the period within
which the strength of the current is governed by inertia
(i. e., the self-induction) rather than by resistance. In
reality the current is not governed either by the self-
induction or by the resistance alone, but by the ratio of
the two. This ratio is sometimes called the " time-con-

212 LECTURES ON THE ELECTROMAGNET.

stant " of the circuit, for it represents the time which
the current takes in that circuit to rise to a definite

fraction of its final value. This definite fraction is the

^

fraction ; or in decimals, 0.634. All curves of rise

of current are alike in general shape they differ only
in scale; that is to say, they differ only in the height to
which they will ultimately rise, and in the time they
will take to attain this fraction of their final value.

Example (1). Suppose E = 10; R = 400 ohms; L = S.
The final value of the current will be 0.025 ampere or 25
milliamperes. Then the time-constant will be 8 * 400 =
l-50th second.

Example (2). The P. O. Standard "A" relay has R = 400
ohms; L 3.25. It works with 0.5 milliampere current, and
therefore will work with 5 Daniell cells through a line of
9,600 ohms. Under these circumstances the time-constant
of the instrument on short circuit is 0.0081 second.

It will be noted that the time-constant of a circuit can
be reduced either by diminishing the self-induction, or
by increasing the resistance. In Fig. 54 the position of
the time-constant for the top curve is shown by the
vertical dotted line at 10 seconds. The current will
take 10 seconds to rise to 0.634 of its final value. This
retardation of the rise of current is simply due to the
presence of coils and electromagnets in the circuit; the
current as it grows being retarded because it has to
create magnetic fields in these coils, and so sets up op-
posing electromotive forces that prevent it from grow-
ing all at once to its full strength. Many electricians
unacquainted with Helmholtz's law have been in the

LECTURES ON THE ELECTROMAGNET. 213

habit of accounting for this by saying that there is a
lag in the iron of the electromagnet cores. They tell
you that an iron core cannot be magnetized suddenly;
that it takes time to acquire its magnetism. They think
it is one of the properties of iron. But we know that
the only true time-lag in the magnetization of iron
that which is properly termed "viscous hysteresis"
does not amount to three per cent, of the whole amount
of magnetization, takes comparatively a long time to
show itself, and cannot therefore be the cause of the
retardation which we are considering. There are also
electricians who will tell you that when magnetization
is suddenly evoked in an iron bar there are induction
currents set up in the iron which oppose and delay its
magnetization. That they oppose the magnetization is
perfectly true; but if you carefully laminate the iron
so as to eliminate eddy currents, you will find, strangely
enough, that the magnetism rises still more slowly to
its final value. For by laminating the iron you have
virtually increased the self-inductive action, and in-
creased the time-constant of the circuit, so that the
currents rise more slowly than before. The lag is not
in the iron, but in the magnetizing current, and the
current being retarded, the magnetization is, of course,
retarded also.

CONNECTING COILS FOR QUICKEST ACTION.

Now let us apply these most important though rather
intricate considerations to the practical problems of
the quick working of the electromagnet. Take the case
of an electromagnet forming some part of the receiving

214 LECTURES ON THE ELECTROMAGNET,

apparatus of a telegraph system, in which it is desired
to secure very rapid working. Suppose the two coils
that are wound upon the horseshoe core are connected
together in series. The coefficient of self-induction for
these two is four times as great as that of either sepa-
rately; coefficients of self-induction being proportional
to the square of the number of turns of wire that sur-
round a given core. Now if the two coils, instead of
being put in series, are put in parallel, the coefficient
of self-induction will be reduced to the same value as if
there were only one coil, because half the line current
(which is practically unaltered) will go through each
coil. Hence the time-constant of the circuit when the
coils are in parallel will be a quarter of that which it is
when the coils are in series; on the other hand, for a
given line current, the final magnetizing power of the
two coils in parallel is only half what it would be with
the coils in series. The two lower curves in Fig. 54 illus-
trate this, from which it is at once plain that the mag-
netizing power for very brief currents is greater when
the two coils are put in parallel with one another than
when they are joined in series.

Now this circumstance has been known for some time
to telegraph engineers. It has been patented several
times over. It has formed the theme of scientific papers
which have been read both in France and in England.
The explanation generally given of the advantage of
uniting the coils in parallel is, I think, fallacious;
namely, that the "extra currents" (i. e., currents due to
self-induction) set up in the two coils are induced in
such directions as tend to help one another when the

LECTURES ON THE ELECTROMAGNET. 215

coils are in series, and to neutralize one another when
they are in parallel. It is a fallacy, because in neither
case do they neutralize one another. Whichever way
the current flows to make the magnetism, it is opposed
in the coils while the current is falling by the so-called
extra currents. If the current is rising in both coils at
the same moment, then, whether the coils are in series
or in parallel, the effect of self-induction is to retard
the rise of the current. The advantage of parallel
grouping is simply that it reduces the time-constant.

BATTERY GROUPING FOR QUICKEST ACTION.

One may consider the question of grouping the bat-
tery cells from the same point of view. How does the
need for rapid working and the question of time-con-
stant affect the best mode of grouping the battery cells ?
The amateur's rule, which tells you to so arrange your
battery that its internal resistance should be equal to
the external resistance, gives you a result wholly wrong
for rapid working. The supposed best arrangement
will not give you (at the expense even of economy) the
best result that might be got out of the given number
of cells. Let us take an example and calculate it out,
and place the results graphically before our eyes in the
form of curves. Suppose the line and electromagnet
have together a resistance of six ohms, and that we have
24 small DanielFs cells, each of electromotive force, say,
one volt, and of internal resistance four ohms. Also
let the coefficient of self-induction of the electromagnet
and circuit be six quadrants. When all the cells are in
series, the resistance of the battery will be 96 ohms, the

LECTURES ON THE ELECTROMAGNET.

total resistance of the circuit 102 ohms, and the full
value of the current 0.235 ampere. When all the cells
are in parallel the resistance of the battery will be 0.133
ohm, the total resistance 6.133 ohms, and the full value
of the current 0.162 ampere. According to the amateur
rule of grouping cells so that internal resistance equals
external, we must arrange the cells in four parallels,
each having six cells in series, so that the internal re-
sistance of the battery will be six ohms, total resistance
of circuit 12 ohms, full value of current 0.5 ampere.

FIG. 55. CURVES OF RISE OF CURRENT WITH DIFFERENT GROUPINGS OF
BATTERY.

Now the corresponding time-constants of the circuit in
the three cases (calculated by dividing the coefficient of
self-induction by the total resistance) will be respect-
ively in series, 0.06 sec.; in parallel, 0.96 sec.; grouped
for maximum steady current, 0.5 sec. From these data
we may now draw the three curves, as in Fig. 55, wherein
the abscissae are the values of time in seconds, and the
ordinates the current. The faint vertical dotted lines
mark the time-constants in the three cases. It will be
seen that when rapid working is required the magnetiz-
ing current will rise, during short intervals of time,

LECTURES ON THE ELECTROMAGNET. 217

more rapidly if all the cells are put in series than it will
do if the cells are grouped according to the amateur
rule.

When they are all put in series, so that the battery
has a much greater resistance than the rest of the cir-
cuit, the current rises much more rapidly, because of the
smallness of the time-constant, although it never attains
the same ultimate maximum as when grouped in the
other way. That is to say, if there is self-induction as
well as resistance in the circuit, the amateur rule does
not tell you the best way of arranging the battery.
There is another mode of regarding the matter which
is helpful. Self-induction, while the current is grow-
ing, acts as if there were a sort of spurious addition to
the resistance of the circuit; and while the current is
dying away it acts of course in the other way, as if there
were a subtraction from the resistance. Therefore you
ought to arrange the batteries so that the internal resist-
ance is equal to the real resistance of the circuit, plus
the spurious resistance during that time. But how
much is the spurious resistance during that time? It
is a resistance proportional to the time that has elapsed
since the current was turned on. So then it comes to
the question of the length of time for which you want
to work it. What fraction of a. second do you require
your signal to be given in ? What is the rate of the
vibrator of your electric bell ? Suppose you have settled
that point, and that the short time during which the
current is required to rise is called t; then the apparent
resistance at time t after the current is turned on is
given by the formula:

218 LECTURES ON THE ELECTROMAGNET.

-I

R t = R x e L -

TIME-CONSTANTS OF ELECTROMAGNETS.

I may here refer to some determinations made by M.
Vaschy, 4 respecting the coefficients of self-induction of
the electromagnets of a number of pieces of telegraphic
apparatus. Of these I must only quote one result, which
is very significant; it relates to the electromagnet of a
Morse receiver of the pattern habitually used on the
French telegraph lines.

Z,, in quadrants.

Bobbins, separately, without iron cores 0.233 and 0.265

Bobbins, separately, with iron cores 1.65 and 1.71

Bobbins, with cores joined by yoke, coils in series 6.37

Bobbins, with armature resting on poles 10.68

It is interesting to note how the perfecting of the
magnetic circuit increases the self-induction.

Thanks to the kindness of Mr. Preece, I have been
furnished with some most valuable information about
the coefficients of self-induction, and the resistance of
the standard pattern of relays and other instruments
which are used in the British postal telegraph service,
from which data one is able to say exactly what the
time-constants of those instruments will be on a given
circuit, and how long in their case the current will take
to rise to any given fraction of its final value. Here let
me refer to a very capital paper by Mr. Preece in an old
number of the "Journal of the Society of Telegraph
Engineers," a paper ff On Shunts," in which he treats
this question, not as perfectly as it could now be treated

4 " Bulletin de la SocietS Internationale des Electriciens," 1886.

LECTURES ON THE ELECTROMAGNET. 219

with the fuller knowledge we have in 1890 about the
coefficients of self-induction, but in a very useful and
practical way. He showed most completely that the
more perfect the magnetic circuit is though, of course,
you are getting more magnetism from your current
the more is that current retarded. Mr. Preece's mode
of experiment was extremely simple; he observed the
throw of the galvanometer, when the circuit which con-
tained the battery and the electromagnet was opened by
a key which at the same moment connected the electro-

Q

502 26

FIG. 56. ELECTROMAGNETS OF RELAY, AND THEIR EFFECTS.

magnet wires to the galvanometer. The throw of the
galvanometer was assumed to represent the extra cur-
rent which flowed out. Fig. 56 represents a few of the
results of Mr. Preece's paper. Take from an ordinary
relay a coil, with its iron core, half the electromagnet,
so to speak, without any yoke or armature. Connect it
up as described, and observe the throw given to the
galvanometer. The amount of throw obtained from the
single coil was taken as unity, and all others were com-
pared with it. If you join up two such coils as they
are usually joined, in series, but without any iron yoke
across the cores, the throw was 17. Putting the iron

20 LECTURES ON THE ELECTROMAGNET.

yoke across the cores, to constitute a horseshoe form,
496 was the throw; that is to say, the tendency of this
electromagnet to retard the current was 496 times as
great as that of the simple coil. But when an armature
was put over the top the effect ran up to 2,238. By
the mere device of putting the coils in parallel, instead
of in series, the 2,238 came down to 502, a little less
than the quarter value which would have been expected.
Lastly, when the armature and yoke were both of them
split in the middle, as is done in fact in all the standard
patterns of the British Postal Telegraph relays, the
throw of the galvanometer was brought down from 502
to 26. Eelays so constructed will work excessively rap-
idly. Mr. Preece states that with the old pattern of
relay having so much self-induction as to give a galva-
nometer throw of 1,688, the speed of signaling was only
from 50 to 60 words per minute; whereas with the
standard relays constructed on the new plan, the speed
of signaling is from 400 to 450 words per minute. It
is a very interesting and beautiful result to arrive at
from the experimental study of these magnetic circuits.

SHORT CORES VERSUS LONG CORES.

In considering the forms that are best for rapid ac-
tion, it ought to be mentioned that the effects of hys-
teresis in retarding changes in the magnetization of
iron cores are much more noticeable in the case of
nearly closed magnetic circuits than in short pieces.
Electromagnets with iron armatures in contact across
their poles will retain, after the current has been cut
off, a very large part of their magnetism, even if the

LECTURES ON THE ELECTROMAGNET. 221

cores be of the softest of iron. But so soon as the arma-
ture is wrenched off the magnetism disappears. An air-
gap in a magnetic circuit always tends to hasten de-
magnetizing. A magnetic circuit composed of a long
air path and a short iron path demagnetizes itself much
more rapidly than one composed of a short air path and
a long iron path. In long pieces of iron the mutual
actions of the various parts tend to keep in them any
magnetization that they may possess; hence they are
less readily demagnetized. In short pieces where these
mutual actions are feeble, or almost absent, the mag-
netization is less stable and disappears almost instantly
on the cessation of the magnetizing force. Short bits
and small spheres of iron have no "magnetic memory/'
Hence the cause of the commonly received opinion
among telegraph engineers that for rapid work electro-
magnets must have short cores. As we have seen, the
only reason for employing long cores is to afford the
requisite length for winding the wire which is neces-
sary for carrying the needful circulation of current to
force the magnetism across the air-gaps. If, for the
sake of rapidity of action, length has to be sacrificed,
then the coils must be heaped up more thickly on the
short core's. The electromagnets in American patterns
of telegraphic apparatus usually have shorter cores and
a relatively greater thickness of winding upon them
than those of European patterns.

222 LECTURES ON THE ELECTROMAGNET.

LECTURE IV.

ELECTROMAGNETIC MECHANISM.

THE task before me to-night comprises the following
matters: First, to speak of that particular variety of
the electromagnet in which the iron core, instead of
being attached to the coils, is movable, and is attracted
into them. Secondly, to speak of the modes of equaliz-
ing the pull of electromagnets of various sorts over their
range of action. Thirdly, to describe sundry mechan-
isms which depend on electromagnets. Lastly, to dis-
cuss the modes of prevention or diminution of the spark-
ing which is so almost invariably found to accompany
the break of circuit when one is using an electromagnet.

THE COIL-AND-PLUNGER.

First, then, let me deal with the apparatus wherein
an iron core is attracted into a tubular coil or solenoid,
an apparatus which, for the sake of brevity, I take the
liberty of naming as the coil-and-plunger. Now, from
quite early times, from 1822 at any rate, it was known
that a coil would attract a piece of iron into it, and that
this action resembled somewhat the action of a piston
going into a cylinder resembled it, I mean to say, in
possessing an extended range of action. The use of
such a device as the coil-and-plunger was even patented

LECTURES ON THE ELECTROMAGNET. 223

in this country in 1846 under the name of " a new elec-
tromagnet." Electromagnetic engines, or motors, were
made on this plan by Page, and afterward by others,
and it became generally known as a distinct device.
But even now, if you inquire into the literature of the
text-books to know what are the peculiar properties of
the coil-and-plunger arrangement, you will find that the
books give you next to no information. They are con-
tent to deal with the thing in very general terms by
saying: Here is a sort of sucking magnet; the core is
attracted in. Some books go so far as to tell you that
the pull is greatest when the core is about half way in ;
a statement which is true in one particular case, but
false in a great many others. Another book tells you
that the pull is greatest at a point one centimetre below
the centre of the coil, for plungers of all different lengths
which is quite untrue. Another book tells you that
a wide coil pulls less powerfully than a narrow one; a
statement which is true for some cases and not for
others. The books also give you some approximate
rules, which, however, are very little to the point. The
reason why this ought to receive much more careful
consideration is because in this mechanism of coil-and-
plunger we have a real means not only of equalizing,
but also of vastly extending the range of the pull of the
electromagnet. Let us take a very simple example for
the sake of contrasting the range of action of the ordi-
nary electromagnet with the range of action of the coil-
and-plunger.

Here are some numbers which are given in a paper
with which I have long been familiar, a paper read by

224

LECTURES ON THE ELECTROMAGNET.

the late Mr. Eobert Hunt in 1856, before the Institution
of Civil Engineers, with that eminent engineer, Eobert
Stephenson, in the chair. Mr. Hunt described the vari-
ous types of motors, and spoke of this question of the
range of action. He recounted some experiments of
his own in which the following was the range of action.

There was a horseshoe elec-
tromagnet which at distance
zero that is, when its arma-
ture was in contact pulled
with a pull of 220 pounds;
when the distance was made
only y-oVoth of an inch (4
mils), the pull fell to 90
pounds; and when the dis-
tance was increased to 20
mils, T V tn f an inch)? the
pull fell to only 36 pounds.
The difference from 220 to
36 was within a range of
g^th of an inch. He con-
trasts this with the results
given by another mechanism, not quite the simple coil-
and-plunger, but a variety of electromagnet brought out
about the year 1845 by a Dane, living in Liverpool,
named Hjorth, wherein a sort of hollow, truncated cone
of iron (Fig. 57), with coils wound upon it a hollow
electromagnet, in fact was caused to act on another
electromagnet, one being caused to plunge into the
other. Now we have no information what the pull was
at distance zero with this curious arrangement of

FIG. 57. HJORTH'S ELECTROMAG-
NETIC MECHANISM.

LECTURES ON THE ELECTROMAGNET. 225

Hjorth's, bat at a distance of one inch the pull (with
a very much larger apparatus than Hunt's) was 160
pounds, the pull at three inches was 88 pounds, at five
inches 72 pounds. Here, then, we have a range of action
going not over g^th of an inch, but over five inches, and
falling not from 220 to 36, but from 160 to 72, obviously
a much more equable kind of range. At the Institution
of Civil Engineers on that occasion a number of the
most celebrated men, Joule, Cowper, Sir William Thom-
son, Mr. Justice Grove, and Prof. Tyndall, discussed
these matters discussed them up and down from the
point of view of range of action, and from the point of
view of the fact that there was no means of working
them at that time except by the consumption of zinc in
a primary battery; and they all came to the conclusion
that electric motors would never pay. Robert Stephen-
son summed up the debate at the end in the following
words: "In closing the discussion," he remarked,
"there could be no doubt from what had been said that
the application of voltaic electricity, in whatever shape it
might be developed, was entirely out of the question
commercially speaking. Without, however, considering
the subject in that point of view, the mechanical appli-
cations seemed to involve almost insuperable difficulties.
The power exhibited by electromagnetism, though very
great, extended through so small a space as to be prac-
tically useless. A powerful magnet might be compared.,
for the sake of illustration, to a steam engine with an
enormous piston but with an exceedingly short stroke ;
such an arrangement was well known to be very undesir-
able."

226 LECTURES ON THE ELECTROMAGNET.

Well, from the discussion in 1856 when this ques-
tion of the length of range was so distinctly set forth
down to the present, there have been a large number of
attempts to ascertain exactly how to design a long range
electromagnet, and those who have succeeded have, as a
general rule, not been the theorists; rather they have
been men compelled by force of circumstances to arrive
at their result by some kind of shall we call it " de-
signing eye," by having a sort of intuitive perception of
what was wanted, and going about it in some rough-
and-ready way of their own. Indeed, I am afraid had
they tried to get much light from calculations based on
orthodox notions respecting the surface distribution
of magnetism, and all that kind of thing, they would
not have been much helped. There is our old friend,
the law of inverse squares, which would of course turn
up the first thing, and they would be told that it would
be impossible to have a magnet that pulled equally
through any range, because the pull was certain to vary
inversely according to the square of the distance. I
noticed that, in a report of my second lecture in one of
the London journals, I am announced to have said that
the law of inverse squares did not apply to electric-
forces. I beg to remark I have said no such thing. It
is well to be precise as to what one does say. There
has been a lively discussion going on quite lately whether
sound varies as the square of the distance or rather,
whether the intensity of it does and the people who
dispute on both sides of the case do not seem to know
what the law of inverse squares means. I have also seen
the statement made last week in the columns of The

LECTURES ON THE ELECTROMAGNET. 227

Times, by one who is supposed to be an eminent author-
ity on eyesight, that the intensity of the color of a scar-
let geranium varies inversely with the square of the dis-
tance from which you s6e it. More utter nonsense was
never written. The fact is, the law of inverse squares,
which is a perfectly true mathematical law, is true not
only for electricity, but for light, for sound, and for
everything else, provided it is applied to the one case to
which a law of inverse squares is applicable. That law
is a law expressing the way in which action at a distance
falls off when the thing from which the action is pro-
ceeding is so small compared with the distance in ques-
tion that it may be regarded as a point. The law of
inverse squares is the law universal of action proceeding
from a point. The music of an orchestra at 10 feet
distance is not four times as loud as at 20 feet distance;
for the size of an orchestra cannot be regarded as a
mere point in comparison with these distances. If you
can conceive of an object giving out a sound, and the
object being so small in relation to the distance at which
you are away from it that it is a point, the law of in-
verse squares is all right for that, not for the intensity
of your hearing, but for the intensity of that to which
your sensation is directed. In no case, however, are
sensations absolutely proportional to their causes. When
the magnetic action proceeds from something so small
that it may be regarded as a point compared with the
distance, then the law of inverse squares is necessarily
and mathematically true.

You may remember that I produced an apparatus
(Fig. 27) which I said was. the only apparatus hitherto

228 LECTURES ON THE ELECTROMAGNET.

devised which did directly prove, experimentally, the
law of inverse squares for the case of a magnetic pole.
There was in it a pole, virtually a point at a considera-
ble distance from a small magnetic needle, which was
also virtually a point.

The law of inverse squares is true ; but it is not what
one works with when one deals with electromagnets
having ends of a visible size, acting on armatures them-
selves of visible sizes, and quite close to them. If you
take a case which never occurs in practice, an armature
of hard steel, permanently magnetized, so far away from
an electromagnet (or rather from one pole only) that
the distance between the one pole and the armature on
which you are acting is so very great compared with
each of them that each of them may be regarded by
comparison as a point, then the law of inverse squares
may be rightly applied, but not unless.

Now we want to arrive at a true law. We want to
know exactly what the law of action of the coil-and-
plunger is. It is not a very difficult thing to work out,
provided you get hold of the right ideas. We must
begin with a simple case, that of a short coil consisting
of but one turn, acting on a single point pole. From
this we may proceed to consider the effect on a point
pole of a long tube of coil. Then we may go on to a
more complex case of the tube coil acting on a very long
iron core; and last of all from the very long iron core
we may pass to the case of a short core.

You all know how a long tube of coil such as this
will act on an iron core. Let us make an experiment
with it, I turn on the current so that it circulates

LECTURES ON THE ELECTROMAGNET. 229

around the coil along the tube, and when I hold in front
of the aperture of the tube this rod of soft iron, it is
sucked into the coil. When I pull it out a little way
it runs back, as with a spring. The current happens to
be a strong one 'about 25 amperes; there are about 700
turns of wire on the coil. The rod is about one inch in
diameter and 20 inches long. So great is the pull that
I cannot pull it entirely out. The pull was very small
when the rod was outside, but as soon as it gets in it is
pulled actively, runs in and settles down with the ends
equally protruding. The tubular coil I have been using
is about 14 inches long; but now let us consider a
shorter coil. Here is one only half an inch from one
end to the other, but I have one somewhere still shorter,
so short that the length, parallel to the axis, is very
small compared with the diameter of the aperture with-
in. The wire on it consists of but one single turn.
Taking such a coil, treating it as only one single ring,
with the current going once round, in what way does it
act on a magnet that is placed on the axis ? First of
all, take the case of a very long permanently magnet-
ized steel magnet, so long, indeed, that any action on
the more distant pole is so feeble that it may be disre-
garded altogether and only one pole, say the north pole,
is near the coil. In what way will that single turn of
coil act on that single pole ? This is the rule, that the
pull does not vary inversely as the square of the dis-
tance, nor as any power at all of the distance measured
straight along the axis, but inversely as the cube of the
slant distance. Let the point in Fig. 58 represent
the centre of the ring, its radius being y. The line OP

230 LECTURES ON THE ELECTROMAGNET.

is the axis of the ring, and the distance from to P
we will call x. The slant distance from P to the ring
we call a. Then the pull on the axis toward the centre
of this coil varies inversely as the
cube of a. That law can be plotted
out in a curve for the sake of ob-
serving the variations of pull at
various points along the axis. Al-
low me to draw your attention to
FIG. 58. ACTION OF SINGLE Fig. 59, which represents a section

COIL ON POINT POLE ON Qr ed y j ew of the coil> At yari _

ous distances right and left of the
coil are plotted out vertically the corresponding force,
the calculations being made for a current of 10 amperes,
circulating once around a ring of one centimetre radius.
The force with which such a current acts on a magnetic
pole of unit strength placed at the central point is 6.28
dynes. If the pole is moved away down the axis, the
pull is diminished; at a distance away equal in length to

O.M7 0;1S 0.13

4 6 a

FIG. 59. ACTION ALONG Axis OF SINGLE COIL.

the radius it has fallen to 2.22 dynes. At a distance
equal to twice the radius, or one diameter, it is only 0.56
dyne, less than one-tenth of what it was at the centre.
At two diameters it has fallen to 0.17 dyne, or less than
three per cent.; and the force at three diameters is only
about two per cent, of that at the centre.

LECTURES ON THE ELECTROMAGNET. 23l

If, then, we could take a very long magnet, we may
utterly neglect the action on the distant pole. If I had
a long steel magnet with the south pole five or six feet
away, and the north pole at a point three diameters
(i. e., six centimetres in this case) distant from the mouth
of the coil, then the pull of the current in one spiral on
the north pole three diameters away would be practi-
cally negligible; it would be less than two per cent, of
what the pull would be of that single coil when the pole
was pushed right up into it. But now, in the case of
the tubular coil, consisting of at least a whole layer of
turns of wire, the action of all of the turns has to be
considered. If the nearest of the turns of wire is at a dis-
tance equal to three diameters, all the other turns of
wire will be at greater distances, and, therefore, if we
may neglect such small quantities as two per cent, of
the whole amount, we may neglect their action also; for
it will be still smaller in amount. Now, for the pur-
pose of arriving at the action of a whole tube of coil, I
will adopt a method of plotting devised by Mr. Sayers.
Suppose we had a whole tube coiled with copper wire
from end to end, its action would be practically the
same as though the copper wire were gathered together
in small numbers at distant intervals? If, for example,
I count the number of turns in a centimetre length of
the actual tubular coil, which I used in my first experi-
ment, I find there are four. Now if, instead of having
four wires distributed over the centimetre, I had one
stout wire in the middle of that space to carry four
times the current, the general effect would be the same.
This diagram (Fig. 60) is calculated out on the sup-

232

LECTURES ON THE ELECTROMAGNET.

position that the effect will be not greatly different if
the wires were aggregated in that way, and it is easier
to calculate. If, beginning at the end of the tube
marked A, we take the wires over the first centimetre of
length and aggregate them, we can draw a curve,
marked 1, for the effect of that lot of wires. For the
next lot we could draw a similar curve, but instead of
drawing it on the horizontal line we will add the several
heights of the second curve on to those of the first, and
that gives the curve marked 2; for the third part add
the ordinates of another similar curve, and so gradually

6/

FIG. 60. ACTION OF TUBULAR COIL.

build up a final curve for the total action of this tubu-
lar coil on a unit pole at different points along the axis.
This resultant curve begins about 2^ diameters away
from the end, rises gently, and then suddenly, and then
turns over and becomes nearly flat with a long level
ba.ck. It does not rise any more after a point about 2^
diameters along from A; the curve at that point be-
comes practically flat, or does not vary more than about
one per cent., however long the tube may be. For ex-
ample, in a tubular coil one inch in diameter and 20
inches long, there will be a uniform magnetic field for
about 15 inches along the middle of the coil. In a

LECTURES ON THE ELECTROMAGNET. 33

tubular coil three centimetres in diameter and 40
centimetres long, there will "be a uniform magnetic field
for about 32 centimetres along the middle of the coil.
The meaning of this is that the value of the magnetic
forces down the axis of that coil begins outside the
mouth of the tube, increases, rises to a certain maxi-
mum amount a little within the mouth of the tube, and
after that is perfectly constant nearly all the way along
the tube, and then falls off symmetrically as you get to
the other end. The ordinates drawn to the curve rep-
resent the forces at corresponding points along the axis
of the tube, and may be taken to represent not simply
the magnetizing force, but the pull on a magnetic pole
at the end of an indefinitely long, thin steel magnet of
fixed strength.

The rule for calculating the intensity of the magnetic
force at any point on the axis of the long tubular coil with-
in this region where the force is uniform is : H = ^ X the

ampere turns per centimetre of length. And, as the
total magnetizing power of a tubular coil is proportional
not only to the intensity of the magnetic force at any point,
but also to the length, the integral magnetizing effect on a
piece of iron that is inserted into the coil may be taken as

practically equal to TT X the total number of ampere turns

in that portion of the tubular coil which surrounds the
iron. If the iron protrudes as much as three diameters at

both ends, the total magnetizing force is simply TT X the
whole number of ampere turns.

Now that case is of course not the one we are usually

LECTURES ON THE ELECTROMAGNET.

dealing with. We cannot procure steel magnets with
unalterable poles of fixed strength. Even the hardest
steel magnet, magnetized so as to give us a permanent
pole near or at the end of it quite close up to the end
of it when you put it into a magnetizing coil becomes
by that fact further magnetized. Its pole becomes
strengthened as it is drawn in, so that the case of an
unalterable pole is not one which can actually be real-
ized. One does not usually work with steel; one works
with soft iron plungers which are not magnetized at all
when at a distance away, but become magnetized in the
act of being placed at the mouth of the coil, and which
become more highly magnetized the further they go in.
They tend, indeed, to settle down, with the ends pro-
truding equally, for that is the position where they most
nearly complete the magnetic circuit; where, therefore,
they are most completely and highly magnetized. Ac-
cordingly we have this fact to deal with, .and whatever
may be the magnetizing forces all along the tube, the
magnetism of the entering core will increase as it goes
on. We must therefore have recourse to the following
procedure: We will construct a curve in which we will
plot not simply the magnetizing forces of the spiral at
different points, but the product of the magnetizing
forces into the magnetism of the core which itself in-
creases as the core moves in. The curve with a flat top
to it corresponds to an ideal case of a single pole of
constant strength. We wish to. pass from this to a curve
which shall represent a real case, with an iron core.
Let us still suppose that we are using a very long core,
one so long that when the front pole has entered the

LECTURES ON THE ELECTROMAGNET. 235

coil the other end is still a long way off. With an iron
core of course it depends on the size and quality of the
iron as to how much magnetism you get for a given
amount of magnetizing power. When the core has en-
tered up to a certain point you have all the magnetizing
forces up to that point acting on it; it acquires a cer-
tain amount of magnetism, so that the pull will neces-
sarily go on increasing and increasing, although the in-
tensity of the magnetic force from point to point along

o

FIG. 61. DIAGRAM OF FORCE AND WORK OP COIL-AND-PLUNGER.

the axis of the coil remains the same, until within
about two diameters from the far end. Although the
magnetic force inside the long spiral remains the same,
because the magnetism of the core is increasing, the
pull goes on increasing and increasing (if the iron does
not get saturated) at an almost uniform rate all the
way up until the piece of iron has been poked pretty
nearly through to the distant end. In Fig. 61 a tubu-
lar coil, B A, is represented. Suppose a long iron core
is placed on the axis to the right, and that its end is

236 LECTURES ON THE ELECTROMAGNET.

gradually brought up toward B. When it arrives at X
the pnll becomes sensible, and increases at first rapidly,
as the core enters the mouth of the tube, then gently,
as the core travels along, attaining a maximum, C,
about at the further end, A, of the tube. When it ap-
proaches to the other end, A, it comes to the region
where the magnetizing force falls off, but the magnetism
is still going on increasing, because something is still
being added to the total magnetizing power, and these
two effects nearly balance one another, so that the pull
arrives at the maximum. This is the highest point, (7,
on the curve ; the greatest pull occurring just as the end
of the iron core arrives at the bottom or far end of the
tubular coil ; from which point there is a very rapid
falling off. The question of rapidity of descent from
that point depends only on how long the core is. If
the core is a very long one, so that its other pole is still
very far away, you have a long, slow descent going on
over some three diameters, and gradually vanishing.
If, however, the other pole is coming up within measur-
able distance of B, then the curve will come down more
rapidly to a definite point, X\. To take a simple case
where the iron core is twice as long as the coil, its curve
will descend in pretty nearly a straight line down to a
point such that the ends of the iron rod stand out
equally from the ends of the tube.

Precisely similar effects will occur in all other cases
where the plunger is considerably longer than (at least
twice as long as) the coil surrounding it. If you take a
different case, however, you will get another effect.
Take the case of a plunger of the same length as the

LECTURES ON THE ELECTROMAGNET. 237

coil, then this is what necessarily happens. At first the
effects are much the same; but as soon as the core has
entered about half, or a little more than half, its length
you begin to have the action of the other pole that is
left protruding outside tending to pull the plunger
back ; and although the magnetizing force goes on in-
creasing the further the plunger enters, the repulsion
exerted by the coil on the other pole of the plunger
keeps increasing still faster as this end nears the mouth
of the coil. In that case the maximum will occur at a
point a little further than half way along the coil, and
from that point the curve will descend and go to zero
at A; that is to say, there will be no pull when both
ends of the plunger coincide with the two ends of the
coil. If you take a plunger that is a little shorter than
the coil, then you find that the attraction comes down
to zero at an earlier period still. The maximum pull
occurs earlier, and so does the reduction of the pull to
zero; there being no action at all upon the short core
when it lies wholly within that region of the tube within
which the intensity of the magnetic force is uniform.
That is to say, for any portion of this tube correspond-
ing to the flat top of the curve of Fig. 60, if the plunger
of iron is so short as to lie wholly within that region,
then there is no action upon it; it is not pulled either
way. Now these things can be not only predicted by
the help of such a law as that, but verified by experi-
ment. Here is a set of tubular coils which we use at
the Finsbury Technical College for the purpose of veri-
fying these laws. There is one here about nine inches
long, one about half that length, another just a quarter,

238 LECTURES ON THE ELECTROMAGNET.

They are all made alike in this way, that they have ex-
actly the same weight of copper wire, cut from the same
hank, upon them. There are, of course, more turns on
the long one than on the shorter, because with the
shorter ones each turn requires, on the average, a larger
amount of wire, and therefore the same weight of wire
will not make the same number of windings. We use
that very simple apparatus, a Salter's balance, to meas-
ure the pull exerted down to different distances on
cores of various lengths. You find in every case the
pull increases and becomes a maximum, then dimin-
ishes. We will now make the experiment, taking first
a long plunger, roughly about twice as long as the coil.
The pull increases as the plunger goes down, and the
maximum pull occurs just when the lower end gets to
the bottom ; beyond that the pull is less. Using the
same plunger with these shorter coils, one finds the
same thing, in fact more marked, for we have now a
core which is more than twice the length of the coil.
So we find, taking in all these cases, that the maximum
pull occurs not when the plunger is half way in, as the
books say, but when the bottom end of it is just begin-
ning to come out through the bottom of the coil that
we are using. If, however, we take a shorter plunger,
the result is different. Here is one just the same length
as the coil. With this one the maximum pull does occur
when the core is about half way in; the maximum pull
is just about at the middle. Again, with a very short
core here is one about one-sixth of the length of the
coil the maximum pull occurs as it is going into the
mouth of the coil; and when both ends have gone in so

LECTURES ON THE ELECTROMAGNET. 239

far that it gets into the region of equable magnetic field
there is no more pull on one end than on the other; one
end is trying to move with a certain force down the
tube, arid the other end is trying to move with exactly
equal force up the tube, and the two balance one an-
other. If we carry that to a still more extreme case,
and employ a little round ball of iron to explore down
the tube, you will find this curious result, that the only
place where any pull occurs on the ball is just as it
is going in at the mouth. For about half an inch in
the neck of the coil there is a pull; but there is no pull
down the interior of the tube at all, and there is no
measurable pull outside.

Now these actions of the coil on the core are capable
of being viewed from another standpoint. Every en-
gineer knows that the work done by a force has to be
measured by multiplying together the force and the
distance through which its point of application moves
forward. Here we have a varying force acting over a
certain range. We ought, therefore, to take the amount
of the force at each point, and multiply that by the ad-
jacent little bit of range, averaging the force over that
range, and then take the next value of force with the
next little bit of range, and so consider in small portions
the work done along the whole length of travel. If we
call the length of travel x the element of length must
be called dx. Multiply that by/, the force. The force
multiplied by the element of length gives us the work,
dw, done in that short range. Now the whole work
over the whole travel is made up of the sum of such
elements all added together; that is to say, we have to

240 LECTURES ON THE ELECTROMAGNET.

take all the various values of/, multiply each by its own
short range dx, and the sum of all those, writing/ for

the sum, would be equal to the sum of all the work;
that is to say, the whole work done in putting the thing
together will be written :

w =jfdx.

Now what I want you to think about is this: Here,
say, is a coil, and there is a distant core. Though there
is a current in the coil, it is so far away from the core
that practically there is no action : bring them nearer
and nearer together; presently they begin to act on one
another; there is a pull, which increases as the core en-
ters, then comes to a maximum, then dies away as the
end of the core begins to protrude at the other side.
There is no further pull at all when the two ends stand
out equally. Now there has been a certain total
amount of work done by this apparatus. Every engineer
knows that if we can ascertain the force at every point
along the line of travel the work done in that travel is
readily expressed by the area of the force curve. Think
of the curve X C X\, in Fig. 61, the ordinates of which
represent the forces. The whole area underneath this
curve represents the work done by the system, and
therefore represents equally the work you would have
to do upon it in pulling the system apart. The area
under the curve represents the total work done in at-
tracting in the iron plunger, with a pull distributed over
the range X X\.

Now I want you to compare that with the case of an

LECTURES ON THE ELECTROMAGNET. 241

electromagnet where, instead of having this distributed
pull, you have a much stronger pull over a much shorter
range. I have endeavored to contrast the two in the
other curves drawn in Fig. 61. Suppose we have our
coil, and suppose the core, instead of being made of one
rod such as this, were made in two parts, so that they
could be put together with a screw in the middle, or
fastened together in any other mechanical way. Now
first treat this rod as a single plunger, screw the two
parts together, and begin with the operation of allow-
ing it to enter into the coil ; the work done will be the
area under the curve which we have already considered.
Let us divide the iron core into two. First of all put
in one end of it ; it will be attracted up in a precisely
similar fashion, only, being a shorter bar, the maximum
would be a little displaced. Let it be drawn in up to
half way only.; we have now a tube half filled with iron,
and in doing so we shall have had a certain amount of
work done by the apparatus. As the piece of iron is
shorter, the force curve, which ascends from ^to Y\ 9
will lie a little lower than the curve XC X\ ; but the
area under that lower curve, which stops half way, will
be the work done by the attraction of this half core.
Now go to the other end and put in the other half of
the iron You now have not only the attraction of the
tube, but that of the piece which is already in place,
acting like an electromagnet. Beginning with a gentle
attraction, it soon runs up, and draws the force curve to
a tremendously steep peak, becoming a very great force
when the distance asunder is very small. We have
therefore in this case a totally different curve made up
16

242 LECTURES ON THE ELECTROMAGNET.

of two parts, a part for the putting in of the first half
of the core, and a steeper part for the second; but the
net result is, we have the same quantity of iron mag-
netized in exactly the same manner by the same quan-
tity of electric current running round the same amount
of copper wire that is to say, the total amount of work
done in these two cases is necessarily equal. Whether
you allow the entire plunger to come in by a gentle pull
over a long range, or whether you put the core in in two
pieces one part with a gentle pull and the other with
a sudden spring up at the end the total work must be
the same; that is to say, the total area under our two
new curves must be the same as the area under the old
curve. The advantage, then, of this coil-and-plunger
method of employing iron and copper is, not that it gets
any more work out of the same expenditure of energy,
but that it distributes the pull over a considerable range.
It does not, however, equalize it altogether over the
range of travel.

A number of experimental researches have been made
from time to time to elucidate the working of the coil-
and-plunger. Hankel, in 1850, examined the relation
between the pull in a given portion of the plunger and
the exciting power. He found that, so long as the iron
core was so thick and the exciting power so small that
magnetization of the iron never approached saturation,
the pull was proportional to the square of the current,
and was also proportional to the square of the number
of turns of wire. Putting these two facts together, we
get the rule which is true only for an unsaturated core
in a given position that the pull is proportional to the

\ V t ,

LECTURES ON THE ELECTROMAGNET. 243

square of the ampere turns. This might have been ex-
pected, for the magnetism of the iron core will, under
the assumptions made above, be proportional to the
ampere turns, and the intensity of the magnetic field in
which it is placed being also proportional to the ampere
turns, the pull, which is the product of the magnetism
and of the intensity of the field, ought to be propor-
tional to the square of the ampere turns.

Dub, who examined cores of different thicknesses,
found the attraction to vary as the square root of the
diameter of the core. His own experiments show that
this is inexact, and that the force is quite as nearly pro-
portional to the diameter as to its square root. There
is again reason for this. The magnetic circuit consists
largely of air paths by which the magnetic lines flow
from one end to the other. As the main part of the
magnetic reluctance of the circuit is that of the air,
anything which reduces the air reluctance increases the
magnetization, and, consequently, the pull. Now, in
this case, the reluctance of the air paths is mainly gov-
erned by the surface exposed by the end portions of the
iron core. Increasing these diminishes the reluctance,
and increases the magnetization by a corresponding
amount. Von Waltenhofen, in 1870, compared the at-
traction exerted by two equal (short) tubular coils on two
iron cores, one of which was a solid cylindrical rod, and
the other a tube of equal length and weight, and found
the two to be more powerfully attracted. Doubtless, the
effect of the increased service in diminishing the reluc-
tance of the magnetic circuit explains the cause of the
observation.

244

LECTURES ON THE ELECTROMAGNET.

Von Feilitzsch compared the action of a tubular coil
upon a plunger of soft iron with that exerted by the
same coil upon a core of hard magnetized steel of equal
dimensions. The plungers (Fig. 62) were each 10.1 cen-
timetres long,, the coil being
29.5 centimetres in length
and 4.2 in diameter. The
steel magnet showed a maxi-
mum attraction when it had
plunged to a depth of five
centimetres, while the iron
core had its maximum at a
depth of seven centimetres,
doubtless because its own
magnetization went on in-
creasing more than did that
of the steel core. As the uni-
form field region began at a
depth of about eight centime-
tres, and the cores were 10.1
centimetres in length, one
would expect the attracting
force to come to zero when
the cores had plunged in to a
MENT ON PLUNGERS OF IRON AND depth of about 18 centime-
tres. Asa matter of fact, the

zero point was reached a little earlier. It will be noticed
that the pull at the maximum was a little greater in
the case of the iron plunger.

The most careful researches of late years are those
made by Dr. Theodore Bruger, in 1886. One of his re-

LECTURES 6$ THE ELECTROMAGNET.

245

searches, in which a cylindrical iron plunger was used,
is represented by two of the curves in Fig. 63. He used
two coils, one 3^ centimetres long, the other seven cen-
timetres long. These are indicated in the bottom left-
hand corner. The exciting current was a little over
eight amperes. The cylindrical plunger was 39 centi-

FIG. 63. BRUGER'S EXPERIMENTS ON
COILS AND PLUNGERS.

FIG. 64. BRUGER'S EXPERIMENTS,
USING CURRENTS OF VARIOUS
STRENGTHS.

metres long. The plunger is supposed, in the diagram,
to enter on the left, and the number of grammes of pull
is plotted out opposite the position of the entering end
of the plunger. As the two curves show by their steep
peaks, the maximum pull occurs just when the end of
the plunger begins to emerge through the coil, and the
pull comes down to zero when the ends of the core pro-

246 LECTURES ON THE ELECTROMAGNET.

trude equally. In this figure the dotted curves relate to
the use of the longer of the two coils. The height of
the peak, with the coil of double length, is nearly four
times as great, there being double ampere turns of ex-
citation. In some other experiments, which are plotted
in Fig. 64, the same core was used "with a tubular coil 13
centimetres long. Using currents of various strengths,
1.5 ampere, 3, 4.8, 6, or 8 amperes, the pull is of course
different, but broadly, you get the same effect, that the
maximum pull occurs just where the pole begins to
come out at the far end of the tubular coil. There are
slight differences; with the smallest amount of current
the maximum is exactly over the end of the tube, but
with currents rather larger the maximum point comes
a little farther back. When the core gets well saturated,
the force curve does not go on rising so far; it begins
to turn over at an earlier stage, and the maximum place
is necessarily displaced a little way back from the end
of the tube. That was also observed by Von Walten-
hofen when using the steel magnet.

EFFECT OF USING CONED PLUNGERS.

But now, if, instead of employing a cylindrical core,
you employ one that is pointed, you find this completely
alters the position of the maximum pull, for now the
point is insufficient to carry the whole of the magnetic
lines which are formed in the iron rod. They do not
come out at the point, but filter through, so to speak,
along the sides of the core. The region where the mag-
netic lines come up through the iron into the air is no

LECTURES ON THE ELECTROMAGNET. 247

longer a definite "pole" at or near the end of the rod,
but is distributed over a considerable surface; conse-
quently when the point begins to poke its nose out, you
still have a larger portion of iron up the tube, and the
pull, instead of coming to a maximum at that position,
is distributed over a wider range. I am now making
the experiment roughly with my spring balance and a
conical plunger, and I think you will be able to notice
a marked difference between this case and that of the
cylindrical plunger. The pull increases as the plunger
enters, but the maximum is not so well defined with a
pointed core as it is with one that is flat ended. This
essential difference between coned plungers and cylin-
drical ones was discovered by an engineer of the name
of Krizik, who applied his discovery in the mechanism
of the Pilsen arc lamps. Coned plungers were also ex-
amined by Bruger. In Fig. 63 are given the curves that
correspond to the use of a coned iron core, as well as
those corresponding to the use of the cylindrical iron
rod. You will notice that, as compared with the cylin-
drical plunger, the coned core never gave so big a pull,
and the maximum occurred not as the tip emerged, but
when it got a very considerable way out on the other
side. So it is with both the shorter and the longer coil.
The dotted curves in Fig. 64 represent the behavior of
a coned plunger. With the longer coil represented, and
W 7 ith various currents, the maximum pull occurred when
the tip had come a considerable way out; and the posi-
tion of the maximum pull, instead of being brought
nearer to the entering end with a high magnetizing
current, was actually caused to occur further down. The

248 LECTURES ON THE ELECTROMAGNET.

range of action became extended with large currents as
compared with small ones. Bruger also investigated
the case of cores of very irregular shapes, resembling,
for example, the shank of a screw-driver, and found a
very curious and irregular force curve. There is a good
deal more yet to be done, I fancy, in examining this
question of distributing the pull on an attracted core by
altering the shape of it, but Bruger has shown us the
way, and we ought not to find very much difficulty in
following him.

OTHER MODES OF EXTENDING RANGE OF ACTION.

Another way of altering the distribution of the pull is
to alter the distribution of the wire on the coil. In-
stead of having a coned core use a coned coil, the wind-
ing being heaped up thicker at one end than at the
other. Such a coil, wound in steps of increasing thick-
ness, has been used for some years by G-aiffe in his arc
lamp; it has also been patented in Germany by Leu-
pold. M. Treve has made the suggestion to employ an
iron wire coil, so to utilize the magnetism of the iron
that is carrying the current. Treve declares that such
coils possess for an equal current four times the pulling
power. I doubt whether that is so; but even if it were,
we must remember that to drive any given current
through an iron wire, instead of a copper wire of the
same bulk, implies that we must force the current
through six times the resistance; and, therefore, we
shall have to employ six times the horse power to drive
the same current through the iron wire coil, so that

LECTURES ON THE ELECTROMAGNET. 49

there is really no gain. Again, a suggestion has been
made to inclose in an iron jacket the coil employed in
this way. Iron-clad solenoids have been employed from
time to time. But they do not increase the range of
action. What they do is to tend to prevent the falling
off of the internal pull at the region within the mouth
of the coil. It equalizes the internal pull at the expense
of all external action. An iron-clad solenoid has prac-
tically no attraction at all on anything outside of it, not
even on an iron core placed at a distance of half a diam-
eter of the aperture; it is only when the core is inside
the tube that the attraction begins, and the magnetiz-
ing power is practically uniform from end to end. Last
year I wished to make use of this property for some
experiments on the action of magnetism on light, and
for that purpose I had built, by Messrs. Paterson and
Cooper, this powerful coil, which is provided with a
tubular iron jacket outside, and a thick iron disc per-
forated by a central hole covering each end. The mag-
netic circuit around the exterior of the coil is practically
completed with soft iron. With this coil, one may take
it, there is an absolutely uniform magnetic field from
one end of the tube to the other; not falling off at the
ends as it would do if the magnetic circuit had simply
an air return. The whole of the ampere turns of ex-
citing power are employed in magnetizing the central
space, in which therefore the actions are very powerful
and uniform. The coil and its uses were described in
my lecture last year at the Royal Institution on "Opti-
cal Torque/'

250 LECTURES ON THE ELECTROMAGNET.

MODIFICATIONS OF THE COIL-AND-PLUNGER.

In one variety of the coil-and-plunger mechanism a
second coil is wound on the plunger. Hjorth used this
modification, and the same thing has been employed in
several arc lamps. There is a series of drawings upon
this wall depicting the mechanism of ahout a dozen
different forms of arc lamp, all made by Messrs. Pater-
son and Cooper. In one of these there is a plunger
with a coil on it drawn into a tubular coil, the current
flowing successively through both coils. In another
there are two separate coils in separate circuits, one of
thin wire and one of thick, one being connected in
series with the arc, and one in shunt.

DIFFERENTIAL COIL-AND-PLUNGER.

There is a third drawing here, showing the arrange-
ment which was originally introduced by Siemens,
wherein a plunger is drawn at one end into the coil that
is in the main circuit, and at the other end into a coil
that is in shunt. That differential arrangement has
certain peculiar properties of which I must not now
stop to speak in detail. It is obvious that where one
core plunges its opposite ends into two coils, the mag-
netization will depend on both coils, and the resultant
pull will not be simply the difference between the pull
of the two coils acting each separately. There is, how-
ever, another differential arrangement, used in the
Brockie-Pell and other arc lamps, in which there are
two separate plungers attached to the two ends of a
see-saw lever. In this case the two magnetizing actions

LECTURES ON THE ELECTROMAGNET. 251

are separate. In a third differential arrangement there
is but one plunger and one tubular bobbin, upon which
are wound the two coils, differentially, so that the
action on the plunger is simply due to the difference
between the ampere turns circulating in the two sepa-
rate wires.

COIL-AND-PLUNGER COIL.

When one abandons iron altogether, and merely uses
two tubular coils, one of wide diameter and another of
narrower diameter, capable of entering into the former,
and passes electric currents through both of them, if
the currents are circulating in the same fashion through
both of them they will be drawn into one another.
This arrangement has also been used in arc lamps.
The parallel currents attract one another inversely, not
as the square of the distance, but approximately as the
distance. This is one of those little details about which
it is as well to be clear. About once a year some kind
friend from a distance writes to me pointing out a little
slip that he says occurs in my book on electricity, in
the passage where I am speaking about the attraction
of parallel wires. I have made the terrible blunder of
leaving out the word square; for I say the attraction
varies inversely as the distance, and my readers are
kind enough to correct me. Now when I wrote that
passage I considered carefully what I had to write, and
the attraction does not vary inversely as the square of
the distance, because two parallel wires dp not act on
one another as two points. They act as two straight
lines or two parallel lines, and the attraction between

252

LECTURES ON THE ELECTROMAGNET.

two parallel lines of current, or two parallel lines of
magnetism, or two parallel lines of anything else that
can attract, will not act inversely as the square, but
simply inversely as the distance in between.

INTERMEDIATE FORMS.

Now this property of the coil-and-plunger of extend-
ing the range of action has been adopted in various
ways by inventors whose object was to try and make

electromagnets with a sort
of intermediate range. For
certain purposes it is desir-
able to construct an electro-
magnet which, while having
the powerful pull of the
electromagnet, should have
over its limited range of
action a more equable pull,
resembling in this respect
the equalizing of range of
the coil-and-plunger. Some
of these intermediate forms
of apparatus are shown in
the following diagrams.
Here (Fig. 65) is a peculiar
form of electromagnet; it combines some of the fea-
tures of the iron-clad electromagnet with those of the
movable plunger; it has a limited range of action, but
is of great power over that range, owing to its excellent
magnetic circuit. It was invented in 1870 by Stevens
and Hardy for use in an electric motor for running

FIG. 65. PLUNGER ELECTROMAGNET
OF STEVENS AND HARDY.

LECTURES ON THE ELECTROMAGNET.

253

sewing machines. A very similar form is used in Wes-
ton's arc lamp. A form of plunger electromagnet in-
vented by Holroyd Smith in 1877 resembles Fig. 65 in-
verted, the coil being surrounded by an iron jacket,
while a plunger furnished at the top with an iron disc
descends down the central tube to meet the iron at the
bottom.

Then there is another variety, of which I was able to
show an example last week by the kindness of the
Brush Company, namely,
the plunger electromagnet
employed in the Brush arc
lamps. A couple of tubular
coils receive each an iron
plunger, connected together
by a yoke; while above, the
magnetic circuit is partially
completed by the sheet of
iron which forms part of the

inclosing box. You have FlG - SG.-ELECTHOMAGNET OF BRUSH

ARC LAMP.

here, also, the advantage of

a fairly complete magnetic circuit, together with a com-
paratively long travel of the plunger and coil. It is a
fair compromise between the two ways of working.
The pull is not, however, in any of these forms, equal
all along the whole range of travel; it increases as the
magnetic circuit becomes more complete.

There are several other intermediate forms. For ex-
ample, one inventor, Gaiser, employs a horseshoe elec-
tromagnet, the cores of which protrude a good distance
beyond the coils, and for an armature he employs a

254

LECTURES ON THE ELECTROMAGNET.

piece of sheet iron, bent round so as to make at its ends
two tubes, which inclose the poles, and are drawn down
over them. Contrast with this design one of much
earlier date by an engineer, Roloff, who made his elec-
tromagnets with iron cores not standing out, but sunk
below the level of the ends of the coils, while the arma-
ture was furnished with little extensions that passed
down into these projecting tubular ends of the coils.
Some arc lamps have magnets of
precisely that form, with a short
plunger entering a tubular coil,
and met half-way down by a short
fixed core inside the tube.

Here (Fig. 67) is one form of
tubular iron-clad electromagnet
that deserves a little more atten-
tion, being the one used by Messrs.
Ayrton and Perry in 1882; a coil
has an iron jacket round it, and
also an annular iron disc across the
top, and an annular iron disc across
the bottom, there being also a short
internal tube of iron extending a little way down from
the top, almost meeting another short internal tube of
iron coming up from the bottom. The magnetic effect
of the inclosed copper coil is concentrated within an
extremely short space, between the ends of the internal
tubes, where there is a wonderfully strong uniform field.
The range of action you can alter just as you please
in the construction by shortening or lengthening the
internal tubes. An iron rod inserted below is drawn

FIG. 67. AYRTON AND PER-
RY'S TUBULAR IRON-CLAD
ELECTROMAGNET.

LECTURES ON THE ELECTROMAGNET. 255

with great power and equality of pull over the range
from one end to the other of these internal tubes.

ACTION OF MAGNETIC FIELD ON SMALL IKON SPHEKE.

In dealing with the action of tubular coils upon iron
cores, I showed how, when a very short core is placed
in a uniform magnetic field, it is not drawn in either
direction. The most extreme case is where a small
sphere of soft iron is employed. Such a sphere, if
placed in even the most powerful magnetic field, does
not tend to move in any direction if the field is truly
uniform. If the field is not uniform, then the iron
sphere always tends to move from the place where the
field is weak to a place where the field is stronger. A
ball of bismuth or one of copper tends, on the contrary,
to move from a place where the field is strong to a
place where the field is weaker. This is the explanation
of the actions called " dia-magnetic," which were at one
time erroneously attributed to a supposed dia-magnetic
polarity opposite in kind to the ordinary magnetic
polarity. A simple way of stating the facts is to say
that a small sphere of iron tends to move up the slope
of a magnetic field, with a force proportional to that
slope; while (in air) a sphere of bismuth or one of
copper tends, with a feeble force, to move down that
slope; any small piece of soft iron a short cylinder,
for example shows the same kind of behavior as a
small sphere. In some of Ayrton and Perry's coiled-
ribbon ampere-meters and voltmeters, and in some of
Sir William Thomson's current meters, this principle
is applied.

256 LECTURES ON THE ELECTROMAGNET

SECTIONED COILS, WITH PLUNGER.

An important suggestion was made by Page, about
1850, when he designed a form of coil-and-plunger hav-
ing a travel of indefinitely long range. The coiled tube
instead of consisting merely of one coil, excited simul-
taneously throughout its whole length by the current,
was constructed in a number of separate sections or
short tubes, associated together end to end, and fur-
nished with means for turning on the electric current
into any of the sections separately. Suppose an iron
core to be just entering into any section, the current is
turned on in that section, and as the end of the core passes
through it the current is then turned on in the section
next ahead. In this way an attraction may be kept up
along a tube of indefinite length. Page constructed an
electric motor on this plan, which was later revived by
Du Moncel, and again by Marcel Deprez in his electric
" hammer/'

WINDING OF TUBULAR COILS AND ELECTROMAGNETS.

The mention of this mode of winding in sections
leads me to say a few final words about winding in
general. All ordinary coils, whether tubular or pro-
vided with fixed cores, are wound in layers of alternate
right-handed and left-handed spirals. In a preceding
lecture I mentioned the mistaken notion, now dis-
proved, that there is any gain in making all the spirals
right-handed or all left-handed. For one particular
case there is an advantage in winding a coil in sections;
that is to say, in placing partitions or cloisons at inter-

LECTURES ON THE ELECTROMAGNET. 257

vals along the bobbin, and winding the wire so as to
fill up each of the successive spaces between the parti-
tions before passing on from one space to the next.
The case in which this construction is advantageous is
the unusual case of coils that are to be used with cur-
rents supplied at very high potentials. For when cur-
rents are supplied at very high potentials there is a
very great tension exerted on the insulating material,
tending to pierce it with a spark. By winding a coil in
cloisons, however, there is never so great a difference of
potential between the windings on two adjacent layers
as there would be if the layers were wound from end to
end of the whole length of coil. Consequently, there is
never so great a tension on the insulating material be-
tween the layers, and a coil so wound is less likely to be
injured by the occurrence of a spark.

Another variety of winding has been suggested,
namely, to employ in the coils a wire of graduated thick-
ness. It has been shown by Sir William Thomson to
be advantageous in the construction of coils of galva-
nometers to use for the inner coils of small diameter a
thin wire; then, as the diameter of the windings in-
creases, a thicker wire; the thickest wire being used on
the outermost layers; the gauge being thus propor-
tioned to the diameter of the windings. But it by no
means follows that the plan of using graded wire, which
is satisfactory for galvanometer coils, is necessarily good
for electromagnets. In designing electromagnets it is
necessary to consider the means of getting rid of heat ;
and it is obvious that the outer layers are those which
are in the most favorable position for getting rid of

258 LECTURES ON THE ELECTROMAGNET.

this heat. Experience shows that the under layers of
coils of electromagnets always attain a higher tempera-
ture than those at the surface. If, therefore, the inner
layers were to he wound with finer wire, offering higher
resistance, and generating more heat than the outer
layers, this tendency to overheating would be still
more accentuated. Indeed, it would seem wise rather
to reverse the galvanometer plan, and wind electromag-
nets with wires that are stouter on the inner layers and
finer on the outer layers.

Yet another mode of winding is to employ several
wires united in parallel, a separate wire being used for
each layer, their anterior extremities being all soldered
together at one end of the coil, and their posterior ex-
tremities being all soldered together at the other.
Magnetically, this mode of winding presents not the
slightest advantage over winding with a single stout
wire of equivalent section. But it has lately been dis-
covered that this mode of winding with multiple wire
possesses one incidental advantage, namely that its use
diminishes the tendency to sparking which occurs at
break of circuit.

EXTENSION OF RANGE BY OBLIQUE APPROACH.

I now pass to the means which have been suggested
for extending the range of motion, or of modifying its
amount at different parts of the range, so as to equalize
the very unequable pull. There are several such de-
vices, some electrical, others purely mechanical, others
electro-mechanical. First, there is an electrical method.
Andre proposed that, as soon as the armature has begun

LECTURES ON THE ELECTROMAGNET. 259

to move nearer, and comes to the place where it is at-
tracted more strongly, it is automatically to make a
contact, which will shunt off part of the current and
make the magnetism less powerful. Burnett proposed
another means; a number of separate electromagnets
acting on one armature, but as the latter approached
these electromagnets were one after the other cut out of
the circuit. I need not say the advantages of that
method are very hypothetical. Then there is another
method which has been used many times with very
great success, the method of allowing the motion of the
armature to occur obliquely, it being mechanically con-
strained so as to move past, instead of toward the
pole. When the armature is pulled thus obliquely, the
pull will be distributed over a definite wider range.
Here is a little motor made on that very plan. A num-
ber of pieces of iron set on the periphery of a wheel are
successively attracted up sideways. An automatic de-
vice breaks the circuit as every piece of iron comes
near, just at the moment when it gets over the poles,
and the current being cut off, it flies on beyond and
another piece comes up, is also attracted in the same
way, and then allowed to pass. A large number of toy
motors have been made from time to time on this plan.
I believe Wheatstone was the first to devise the method
of oblique approach about the year 1841. He made
many little electromagnetic motors, the armatures of
which were in some cases solid rims of iron arranged
as a sort of wheel, with two or more zigzag internal
teeth, offering oblique surfaces to the attraction of an
electromagnet. Such little motors are often now used

260 LECTURES ON THE ELECTROMAGNET.

for spinning Geissler's vacuum tubes. In these motors
the iron rim is fixed and the electromagnet rotates.
The pole of the electromagnet finds itself a certain dis-
tance away from the iron ring; it tries to get nearer.
The only way it can get nearer is by swinging round,
and so it gradually approaches, and as it approaches
the place where it is nearest to the internal projection
of the rim the current is cut off, and it swings further.
This mode may be likened to a cam in a mechanical
movement. It is, in fact, nothing else than an electro-
magnetic cam. There are other devices too, which are
more like electromagnetic linkage. If you curve the
poles or shape them out, you may obtain actions which
are like that of a wedge on an inclined plane. There
is an electromagnet in one of Paterson and Cooper's arc
lamps wherein the pole-piece, coming out below the
magnet, has a very peculiar shape, and the armature is
so pivoted with respect to the magnet, that as the arma-
ture approaches the core as a whole its surface recedes
from that of the pole-piece, the effect being that the
pull is equalized over a considerable range of motion.
There is a somewhat similar device in De Puydt's pat-
tern of arc lamp.

Here is another device for oblique approach, made by
Froment. In the gap in the circuit of the magnet a
sort of iron wedge is put in, which is not attracted
squarely to either face, but comes in laterally between
guides. Another of Froment's equalizers, or distribu-
tors, consists of a parallel motion attachment for the
armature, so that oblique approach may take place,
without actual contact, Here (Fig. 68) is another me-

LECTURES ON TM ELECTROMAGNET.

561

chanical method of equalizing devised by Froment, and
used by Le Eoux. You know the Stanhope lever, the
object of which is to transform a weak force along a
considerable range into a powerful force of short range.
Here we use it backward. The armature itself, which

FIG. 6& FROMENT'S EQUALIZER WITH
STAN.HOPE LEVER.

FIG. 69. DAVY'S MODE OP CONTROL-
LING ARMATURE BY SPRING.

is attracted with a powerful force of short range, is at-
tached to the lower end of the Stanhope lever, and the
arm attached to the knee of the lever will deliver a dis-
tributed force over quite a different range. One way,
not of equalizing the actual motion over the range, but
of counterbalancing the variable attractive force, is to
employ a spring instead of gravity to control the arma-

262 LECTURES ON THE ELECTROMAGNET.

ture. So far back as 1838, Edward Davy, in one of his
telegraphic patents, described the use of a spring (Fig.
69) to hold back the armature. Davy preceded Morse
in the use of a spring to pull back the armature. There
is a way of making a spring act against an armature
more stiffly as the pull gets greater. In this method
there is a spring with various set screws set up against

FIG. 70. ROBERT HOUDIN'S EQUALIZER.

it, and which come into action at different ranges, so as
to alter the stiffness of the spring, making it virtually
stiffer as the armature approaches the poles. Yet an-
other method is to employ, as the famous conjurer Eobert
Houdin did, a rocking lever. Fig. 70 depicts one of
Robert Houdin's equalizers. The pull of the electro-
magnet on the armature acts on a curved lever which
works against a second one, the point of application of
force between the one and the other altering with their

LECTURES ON THE ELECTROMAGNET.

263

position. When the armature is far away from the
pole, the leverage of the first lever on the second lever
is great. When the armature gets near, the leverage of
the first lever on the second is comparatively small.
This employment of the rocking lever was adopted from
Houdin by Duboscq, and put into the Duboscq arc lamp,
where the regulating mechanism at the bottom of the
lamp contains a rocking lever. Here upon the lecture
table is a Duboscq arc lamp. In this pattern (Fig. 71),

FIG. 71. MECHANISM OF DUBOSCQ'S ARC LAMP.

one lever, B, which is curved, plays against another, A,
which is straight. A similar mechanism is used for
equalizing the action in the Serrin arc lamp, where one
of the springs that holds up the jointed parallelogram
frame is applied at the end of a rocking lever to equalize
the pull of the regulating electromagnet. In this lamp
there is also introduced the principle of oblique approach;
for the armature of the electromagnet is not allowed to
travel straight toward the poles of the magnet, but is
pulled up obliquely past it.

264 LECTURES ON THE ELECTROMAGNET.

Another device for equalizing the pull was used by
Wheatstone in the step-by-step telegraph in 1840. A
hole is pierced in the armature, and the end of the core
is formed into a projecting cone, which passes through
the aperture of the armature, thereby securing a more
equable force and a longer range. The same device has
reappeared in recent years in the form of electromagnet
used in the Thomson-Houston arc lamp, and in the
automatic regulator of the same firm.

POLAEIZED MECHANISM: USES OF PERMANENT

MAGNETS.

We must now turn our attention to one class of elec-
tromagnetic mechanism -which ought to be carefully
distinguished from the rest. It is that class in which,
in addition to the ordinary electromagnet, a permanent
magnet is employed. Such an arrangement is generally
referred to as a polarized mechanism. The objects for
which the permanent magnet is introduced into the
mechanism appear to be in different cases quite differ-
ent. I am not sure whether this is clearly recognized,
or whether a clear distinction has even been drawn be-
tween three entirely separate purposes in the use of a
permanent magnet in combination with an electromag-
net. The first purpose is to secure unidirectionality of
motion; the second is to increase the rapidity of action
and of sensitiveness to small currents; the third to aug-
ment the mechanical action of the current.

(a.) Unidirectionality of Motion. In an ordinary elec-
tromagnet it does not matter which way the current
circulates; no matter whether the pole is north or

LECTURES ON THE ELECTROMAGNET. 265

south, the armature is pulled, and on reversing the cur-
rent the armature is also pulled. There is a rather
curious old experiment which Sturgeon and Henry
showed, that if you have an electromagnet with a big
weight hanging on it, and you suddenly reverse the
current, you reverse the magnetism, but it still holds
the weight up; it does not drop. It has not time to
drop before the magnet is charged up again with mag-
netic lines the other way on. Whichever way the mag-
netism traverses the ordinary soft iron electromagnet,
the armature is pulled. But if the armature is itself a
permanent magnet of steel, it will be pulled when the
poles are of one sort, and pushed when the poles are
reversed that is to say, by employing a polarized arma-
ture you can secure unidirectionality of motion in cor-
respondence with the current. One immediate applica-
tion of this fact for telegraphic purposes is that of
duplex telegraphy. You can send two messages at the
same time and in the same direction to two different
sets of instruments, one set having ordinary electro-
magnets, with a spring behind the armature of soft iron,
which will act simply independently of the direction of
the current, depending only on its strength and dura-
tion; and another set having electromagnets with polar-
ized armatures, which will be affected not by the strength
of the current, but by the direction of it. Accord-
ingly, two completely different sets of messages may be
sent through that line in the same direction at the same
time.

Another mode of constructing a polarized device is to
attach the cores of the electromagnet to a steel magnet,

266 LECTURES ON THE ELECTROMAGNET.

which imparts to them an initial magnetization. Such
initially magnetized electromagnets were used by Brett
in 1848 and by Hjorth hi 1850. A patent for a similar
device was applied for in 1870 by !Sir William Thomson
and refused by the Patent Office. In 1871 S. A. Varley
patented an electromagnet having a core of steel wires
united at their ends.

Wheatstone used a polarized apparatus consisting of
an electromagnet acting on a magnetized needle. He
patented, in fact, in 1845, the use of a needle perma-
nently magnetized to be attracted one way or the other
between the poles of an electromagnet. Sturgeon had
described the very same device in the Annals of Elec-
tricity in 1840. Gloesner claims to have invented the
substitution of permanent magnets for mere armatures
in 1842. In using polarized apparatus it is necessary to
work, not with a simple current that is turned off and
on, but with reversed currents. Sending a current one
way will make the moving part move in one direction;
reversing the current makes it go over to the other side.
The mechanism of that particular kind of electric bell
that is used with magneto-electric calling apparatus
furnishes an excellent example of a polarized construc-
tion. With these bells no battery is used; but there is
a little alternate current dynamo, worked by a crank.
The alternate currents cause the pivoted armature in
the bell to oscillate to right and left alternately, and so
throw the little hammer to and fro between the two
bells.

(>.) Rapidity and Sensitiveness of Action. For relay
work polarized relays are often employed, and have been

LECTURES ON THE ELECTROMAGNET. 267

for many years. Here on the table is one of the post-
office pattern of standard relay, having a steel magnet
to give magnetism permanently to a little tongue or
armature which moves between the poles of an electro-
magnet that does the work of receiving the signals. In
this particular case the tongue of the polarized relay
works between two stops, and the range of motion is made
very small in order that the apparatus may respond to
very small currents. At first sight it is not very appar-
ent why putting a permanent magnet into a thing should
make it any more sensitive. Why should permanent
magnetism secure rapidity of working ? Without know-
ing anything more, inventors will tell you that the pres-
ence of a permanent magnet increases the rapidity with
which it will work. You might suppose that perma-
nent magnetism is something to be avoided in the cores
of your working electromagnets, otherwise the arma-
tures would remain stuck to the poles when once they
had been attracted up. Kesidual magnetism would, in-
deed, hinder the working unless you have so arranged
matters that it shall be actually helpful to you. Now
for many years it was supposed that permanent mag-
netism in the electromagnet was anything but a source
of help. It was supposed to be an unmitigated nuisance,
to be got rid of by all available means, until, in 1855,
Hughes showed us how very advantageous it was to have
permanent magnetism in the cores of the electromag-
net. Here (Fig. 51), is the drawing of Hughes' magnet
to which I referred in Lecture III. A compound per-
manent magnet of horseshoe shape is provided with coils
on its pole-pieces, and there is a short armature on the

2ti8 LECTURES ON THE ELECTROMAGNET.

top attached to a pivoted lever and a counteracting
spring. The function of this arrangement is as follows :
That spring is so set as to tend to detach the armature,
but the permanent magnet has just enough magnetism
to hold the armature on. You can, by screwing up a
little screw behind the spring, adjust these two con-
tending forces> so that they are in the nicest possible
balance; the armature held on by the magnetism, and
the spring just not able to pull it off. If, now, when
these two actions are so nearly balanced you send an
electric current round the coils, if the electric current
goes one way round it just weakens the magnetism
enough for the spring to gain the victory, and up goes
the armature. This apparatus then acts by letting the
armature off when the balance is upset by the electric
current; and it is capable of responding to extremely
small currents. Of course, the armature has to be put
on again mechanically, and in Hughes' type-writing
telegraph instruments it is put on mechanically between
each signal and the next following one. The arrange-
ment constitutes a distinctive piece of electromagnetic
mechanism.

(c.) Augmenting Mechanical Action of Current. The
third purpose of a permanent magnet, to secure a greater
mechanical action of the varying current, is closely
bound up with the preceding purpose of securing sen-
sitiveness of action. It is for this purpose that it is used
in telephone receivers; it increases the mechanical ac-
tion of the current, and therefore makes the receiver
more sensitive. For a long time this was not at all
clear to me, indeed I made experiments to see how far

LECTURES ON THE ELECTROMAGNET. 269

it was due to any variation in the magnetic permeability
of iron at different stages of magnetization, for I found
that this had something to do with it, but I was quite
sure it was not all. Prof. George Forbes gave me
the clue to the true explanation; it lies in the law of
traction with which you are now familiar, that the pull
between a magnet and its armature is proportional to
the square of the number of magnetic lines that come
into action. If we take N, the number of magnetic
lines that are acting through a given area>, then to the
square of that the pull will be proportional. If we
have a certain number of lines, N, coming permanently
to the armature, the pull is proportional to N 2 . Sup-
pose the magnetism now to be altered say made a little
more; and the increment be called dN; so that the
whole number is now N+^N. The pull will now be
proportional to the square of that quantity. It is evi-
dent that the motion will be proportional to the differ-
ence between the former pull and the latter pull. So
we will write out the square of N+^N and the square
of N and take the difference.

Increased pull, proportional to N 2 +2 N<#N+dN 2 ;

Initial pull, proportional to N 2

Subtracting; difference is 2 N^N+^N 2 .

^e may neglect the last term, as it is small com-
pared with the other. So we have, finally, that the
change of pull is proportional to 2 N^N. The altera-
tion of pull between the initial magnetism and the
initial magnetism with the additional magnetism we
have given to it turns out to be proportional not simply

270 LECTURES ON THE ELECTROMAGNET.

to the change of magnetism, but also to the initial num-
ber N, that goes through it to begin with. The more
powerful the pull to begin with, the greater is the
change of pull when you produce a small change in the
number of magnetic lines. That is why you have this
greater sensitiveness of action when using Hughes* elec-
tromagnets, and greater mechanical effect as the result
of applying permanent magnetism to the electromagnets
of telephone receivers.

ELECTROMAGNETIC MECHANISM.

There are some other kinds of electromagnetic mech-
anism to which I must briefly invite your attention
as forming an important part of this great subject.
Of one of these the mention of permanent magnets re-
minds me.

MOVING COIL IN PERMANENT MAGNETIC FIELD.

A coil traversed by an electric current experiences
mechanical forces if it lies in a magnetic field, the force
being proportional to the intensity of the field. Of this
principle the mechanism of Sir Wm. Thomson's siphon
recorder is a well-known example. Also those galva-
nometers which have for their essential part a movable
coil suspended between the poles of a permanent mag-
net, of which the earliest example is that of Robertson
("Encyclopaedia Britannica," ed. viii., 1855), and of
which Maxwell's suggestion, afterward realized by d'Ar-
sonval, is the most modern. Siemens has constructed
a relay on a similar plan,

LECTURES ON THE ELECTROMAGNET. 271

MAGNETIC ADHERENCE.

There are a few curious pieces of apparatus devised
for increasing adherence electrornagnetically between
two things. Here is an old device of Nickles, who
thought he would make a new kind of rolling gear.
Whether it was a railway wheel on a line, or whether it

FIG. 72. NiCKLEs 1 MAGNETIC FRICTION GEAR.

was going to be an ordinary wheel gearing, communi-
cation of motion was to be made from one wheel to an-
other, not by cogs or by the mere adherence of ordinary
friction, but by magnetic adherence. In Fig. 72 there
are shown two iron wheels rolling on one another, with
a sort of electromagnetic jacket around them, consisting
of an electric current circulating in a coil, and causing

272

LECTURES ON THE ELECTROMAGNET.

them to attract one another and stick together with
magnetic adherence. In Nickles' little book on the
subject there are a great number of devices of this kind
described, including a magnetic brake for braking rail-
way wagons, engines, and carriages, applying electro-
magnets either to the wheels or else to the line, to stop
the motion whenever desired. The notion of using
an electromagnetic brake has been revived quite recently
in a much better form by Prof. Geo. Forbes and Mr.

Timmis, whose particular
form of electromagnet,
shown in Fig. 73, is pecu-
liarly interesting, being a
better design than any I
have ever seen for securing
powerful magnetic traction
for a given weight of iron
and copper. The magnet
is a peculiar one; it is rep-
resented here as cut away to show the internal con-
struction. There is a sort of horseshoe made of one
grooved rim, the whole circle of coil being laid imbed-
ded in the groove. The armature is a ring which is
attracted down all round, so that you have an extremely
compact magnetic circuit around the copper wire at
every point. The magnet part is attached to the frame
of the wagon or carriage, and the ring-armature is at-
tached to the wheel or to its axis. On switching on the
electric current the rim is powerfully pulled, and braked
against the polar surface of the electromagnet.

Forbes' arrangement appears to be certainly the best

FIG. 73. FoRBES 1 ELECTROMAGNET.

LECTURES ON THE ELECTROMAGNET.

273

yet thought of for putting a magnetic brake to the
wheels of a railway train.

Another, but quite distinct, piece of mechanism de-
pending on electromagnetic adherence is the magnetic
clutch employed in Gulcher's arc lamp.

REPULSION MECHANISM.

Then there are a few pieces of mechanism which de-
pend on repulsion. In 1850 a little device was patented
by Brown and Williams, consisting, as shown in Fig.

FIG. 74. ELECTROMAGNETIC MECHAN-
ISM WORKING BY REPULSION.

FIG. 75. -REPULSION BETWEEN Two
PARALLEL CORES.

74, of an electromagnet which repelled part of itself.
The coil is simply wound on a hollow tube, and inside
the coil is a piece, B, of iron, bent as the segment of a
cylinder to fit in, going from one end to the other.
Another little iron piece, A, also shaped as the segment
of a tube, is pivoted in the axis of the coil. When
these are magnetized one tends to move away from the
other, they being both of the same polarity. Of late
there have been many ampere-meters and voltmeters
18

274 LECTURES ON THE ELECTROMAGNET.

made on this plan of producing repulsion between the
parallel cores.

Here (Fig. 75) is another device of recent date, due to
Maikoff and De Kabath. Two cores of iron, not quite
parallel, pivoted at the bottom, pass up through a tubiu
lar coil. When both are magnetized, instead of attract-
ing one another, they open out; they tend to set them-
selves along the magnetic lines through that tube. The
cores, being wide open at the bo.ttom, tend to oper also
at the top.

ELECTROMAGNETIC VIBRATORS.

Then there is a large class of mechanisms about which
a whole chapter might be written, namely, those in
which vibration is maintained electromagnetically. The
armature of an electromagnet is caused to approach and
recede alternately with a vibrating motion, the current
being automatically cut off and turned on again by a
self-acting brake. The electromagnetic vibrator is one
of the cleverest things ever devised. The first vibrat-
ing electromagnetic mechanism ever made was exhibited
here in this room in 1824 by its inventor, an English-
man named James Marsh. It consisted of a pendulum
vibrating automatically between the poles of a perma-
nent magnet. Later, a number of other vibrating de-
vices were produced by Wagner, Neef, Froment, and
others. Most important of all is the mechanism of the
common electric trembling bell, invented by a man
whose very name appears to be quite forgotten John
Mirand. How many of the millions of people who use
electric bells know the name of the man who invented

LECTURES ON THE ELECTROMAGNET. #75

them ? John Mirand, in the year 1850, put the electric
bell practically into the same form in which it has heen
employed from that day to this. The vibrating ham-
mer, the familiar push-button,, the indicator or annun-
ciator, are all of his devising, and may be seen depicted
in the specification of his British patent, just as they
came from his hand.

Time alone precludes me from dealing minutely with
these vibrators, and particularly with the recent work
of Mercadier and that of Langdon-Davies, whose re-
searches have put a new aspect on the possibilities of
harmonic telegraphy. Langdon-Davies' rate governor
is the most recent and perfect form of electromagnetic
vibrator.

INDICATOR MOVEMENTS.

Upon the table here are a number of patterns of elec-
tric bells, and a number also of the electro-mechanical
movements or devices employed in electric bell work,
some of which form admirable illustrations of the vari-
ous principles that 1 have been laying down. Here is
an iron-clad electromagnet; here a tripolar magnet;
here a series of pendulum motions of various kinds;
here is an example of oblique pull; here is Jensen's in-
dicator, with lateral pull; here is Moseley's indicator,
with a co il-and-pl unger, iron-clad; here is a clever de-
vice in which a disc is drawn up to better the magnetic
circuit. Here, again, is Thorpe's semaphore indicator,
one of the neatest little pieces of apparatus, with a sin-
gle central core surrounded by a coil, while a little strip
of iron coming round from behind serves to complete

276 LECTURES ON THE ELECTROMAGNET.

the circuit all save a little gap. Over the gap stands
that which is to be attracted, a flat disc of iron, which,
when it is attracted, unlatches another disc of brass
which forthwith falls down. It is an extremely effect-
ive, very sensitive, and very inexpensive form of annun-
ciator. The next two are pieces of polarized mechanism
having a motion directed to one side or the other, ac-
cording to the direction of the current. From the
backboard projects a small straight electromagnet.
Over it is pivoted a small arched steel magnet, perma-
nently magnetized, to which is attached a small signal
lever bearing a red disc. If there is a current flowing
one way then the magnet that straddles over the pole of
the electromagnet will be drawn over in one direction.
If I now reverse the current the electromagnet attracts
the other pole of the curved magnet. Hence this
mechanism allows of an electrical replacement without
compelling the attendant to walk up to the indicator
board. The polarized apparatus for indicators has this
advantage, that you can have electrical as distinguished
from mechanical replacement.

THE STUDY OF ELECTROMAGNETIC MECHANISM.

The rapid survey of electromagnetic mechanisms in
general has necessarily been very hurried and imperfect.
The study of it is just as important to the electrical
engineer as is the study of mechanical mechanism to
the mechanical engineer. Incomplete as is the present
treatment of the subject, it may sufficiently indicate to
other workers useful lines of progress, and so fitly be
appended to these lectures on. the electromagnet. In a

LECTURES ON THE ELECTROMAGNET. 277

very few years we may expect the introduction into all
large engineering shops of electromagnetic tools. On a
small scale, for driving dental appliances, electromag-
netic engines have long been used. Large machine
tools, electromagnetically worked, have already begun
to make their appearance. Some such were shown at
the Crystal Palace, in 1881, by Mr. Latimer Clark, and
more recently Mr. Rowan, of Glasgow, has devised a
number of more derek>ped forms of electromagnetic
tools.

SUPPRESSION" OF SPAEKING.

It now remains for me to speak briefly of the sup-
pression of sparks. There are some half-dozen differ-
ent ways of trying to get rid of the sparking that occurs
in the breaking of an electric circuit whenever there
are electromagnets in that circuit. Many attempts have
been made to try and get rid of this evil. For instance,
one inventor employs an air blast to blow out the spark
just at the moment it occurs. Another causes the spark
to occur under a liquid. Another wipes it out with a
brush of asbestos cloth that comes immediately behind
the wire and rubs out the spark. Another puts on a
condenser to try and store up the energy. Another tries
to put on a long thin wire or a high resistance of liquid,
or something of that kind, to provide an alternate path
for the spark, instead of jumping across the air and
burning the contacts. There exist some half-score, at
any rate, of that kind of device. But there are devices
that I have thought it worth while to examine and ex-
periment upon, because they depend merely upon the

278 LECTURES ON THE ELECTROMAGNET.

mode of construction adopted in the building of the
electromagnet, and they have each their own qualities.
I have here five straight electromagnets, all wound on
bobbins the same size, for which we shall use the same
iron core and the same current for all. They are all
made, not only with bobbins of the same size, but their
coils consist as nearly as possible of the same weight of
wire. The first one is wound in the ordinary way; the
second one has a sheath of copper wound round the in-
terior of the bobbin before any wire is put on. This
was a device, I believe, of the late Mr. C. F. Varley, and
is also used in the field magnets of Brush dynamos. The
function of the copper sheath is to allow induced cur-
rent to occur, which will retard the fall of magnetism,
and damp down the tendency to spark. The third one
is an attempt to carry out that principle still further.
This is due to an American of the name of Paine, and
has been revived of late years by Dr. Aron, of Berlin.
After winding each layer of the coil, a sheath of metal
foil is interposed so as to kill the induction from layer
to layer. The fourth one is the best device hitherto
used, namely, that of differential winding, having two
coils connected so that the current goes opposite ways.
When equal currents flow in both circuits there is no
magnetism. If you break the circuit of either of the
two wires the core at once becomes magnetized. You
get magnetism on breaking, you destroy magnetism on
making the circuit; it is just the inverse case to that
of the ordinary electromagnet. There the spark occurs
when magnetism disappears, but here, since the mag-
netism disappears when you make the circuit, you do

LECTURES ON THE ELECTROMAGNET. 2ft)

not get any spark at make, because the circuit is already
made. You do not get any at break, because at break
there is no magnetism. The fifth and last of these elec-
tromagnets is wound according to a plan devised by Mr.
Langdon-Davies, to which I alluded in the middle of
this lecture, the bobbin being wound with a number of
separate coils in parallel with one another, each layer
being a separate wire, the separate ends of all the layers
being finally joined up. In this case there are 15 sepa-
rate circuits; the time-constants of them are different,
because, owing to the fact that these coils are of differ-
ent diameters, the coefficient of self-induction of the
outer layers is rather less, and their resistance, because
of the larger size, rather greater than those of the inner
layers. The result is that instead of the extra current
running out all at the same time, it runs out at differ-
ent times for these 15 coils. The total electromotive-
force of self-induction never rises so high and it is un-
able to jump a large air-gap, or give the same bright
spark as the ordinary electromagnet would give. We
will now experiment with these coils. The differential
winding gives absolutely no spark at all, and second in
merit comes No. 5, with the multiple wire winding.
Third in merit comes the coil with intervening layers
of foil. The fourth is that with copper sheath. Last
of all, the electromagnet with ordinary winding.

CONCLUSION.

Now let me conclude by returning to my starting-
point the invention of the electromagnet by William
Sturgeon. Naturally you would be glacL to see the

280 LECTURES ON THE ELECTROMAGNET.

counterfeit presentment of the features of so remark-
able a man, of one so worthy to be remembered among
distinguished electricians and great inventors. Your
disappointment cannot be greater than mine when I
tell you that all my efforts to procure a portrait of the
deceased inventor have been unavailing. Only this I
have been able to learn as the result of numerous in-
quiries; that an oil-painting of him existed a few years
ago in the possession of his only daughter, then resident
in Manchester, whose address is now, unfortunately,
unknown. But if his face must remain unknown to us,
we shall none the less proudly concur in honoring the
memory of one whose presence once honored this hall
wherein we are met, and whose work has won for him
an imperishable name.

UsTDEX.

AIR-GAP, effect of, in magnetic
circuit, 221

effect of, on magnetic reluctance,

117, 119, 144

Andre, equalizing the pull of a mag-
net, 258

Ampere, researches of, 1C
Ampere turns, calculation of, 166
Arago, researches of, 16
Arc lamp mechanism, 54

Brockie-Pell, 250

Brush, 253

De Puydt, 260

Duboscq, 263

Gaiffe, 248

Giilcher, 273

Paterson and Cooper, 250, 260

Pilsen, 247

Serrin, 263

Thomson-Houston, 264

West on, 253

Armature, effect of, on permanent
magnets, 200

effect of shape, 80

length and cross-section of, 196

position and form of, 197

pulled obliquely, 259

round vs. flat, 197
Aron, sheath for magnet coils, 278
Ayrton, distribution of free magnet-
ism, 109

magnetic shunts, 13
Ayrton and Perry's coiled ribbon
voltmeters, 255

tubular electromagnet, 254

T3 AR electromagnet, 49

J' Barlow, magnetism of long

bars, 151

Barlow's wheel, 16
Battery grouping for quickest action,

215

resistance for best effect, 78, 185
used by Sturgeon, 18
Bell (A. G.), iron-clad electromagnet,

135

Bernoulli's rule for traction, 98
Bidwell, electromagnetic pop-gun,

206

measurement of permeability, 68
Bosanquet, investigations of, 90
magneto-motive force, 12
measurement of permeability,

59,63

Brett, polarized magnets, 266
Brisson, method of winding, 184
Brockie-Pell, differential coil-and-

plunger, 250

Brown and Williams, repulsion mech-
anism, 273

Bruger, coils and plungers, 244
Burnett, equalizing the pull of a
magnet, 2L9

/~"1 AMACHCTS electromagnet, 202
^-^ Cancels electromagnet, 202
Cast iron, magnetization of, 56
Clark, electromagnetic tools, 277
Coil-and-plunger coil, 251

diagram of force and work of, 235

differential, 250

282

INDEX.

Coil-and-plunger electromagnet, 50,
222, 228, 242, 244

modifications of, 250
Coil moved in permanent magnetic

field, 270
Coils, effect of position. 192

effect of size, 191

how connected for quickest ac-
tion, 213

Coned plungers, effect of, 246
Cook's experiments, 38
Cores, effect of shape, 80

determination of length, 154

effect of shape of section, 193

hollow versus solid, 78

lamination of, 207, 213

of different thicknesses, 243

of irregular shapes, 248

proper length of, 94, 118

square versus round, 78

tubular, 158
Coulomb, law of inverse squares, 111

two magnet ic fluids, 9
Cowper, lamination of cores, 207

range of action, 225
Gumming, magnetic conductivity, 10

galvanometer, 16
Curves of hysteresis, 75

of magnetization and permeabil-
ity, 71

T~\ 'ARSON VAL, galvanometer, 270
* ' Davy, mode of controlling

armature, 261
Davy, researches of, 16
De La Rive, floating battery and coil,

16

magnetic circuit, 10
Deprez, electric hammer, 256
Diacritical point of magnetization, 74
Diamagnetic action, 255
Dove, magnetic circuit, 10
Dub, best position of coils, 192

cores of different thicknesses, 243
distance between poles, 194

Dub, flat vs. pointed poles, 125, 127
magnetic circuit, 10
magnetism of long bars, 152
polar extensions of core, 126
thickness of armatures, 158

Du Moncel, best position of coils, 192
club-footed electromagnet, 189
distance between poles, 194
effect of polar projections, 198
effect of position of armature, 151
electric motor, 256
electromagnetic pop-gun, 205
experiments with pole-pieces, 132
length of armatures, 158
on armatures, 197
tubular cores, 159

THLECTRIC bells, 275

Jr^ invented by Mirand, 274

Electric indicators, 275

motors, not practicable, 225
Electromagnet, Ayrton and Perry's,
254

bar, 49, 188

Camacho's, 202

Cancels, 202

club-footed, 189

coil-and-plunger, 50, 222

coils, resistance of, 78

design of, for various uses, 9

Du Moncel's, 189

Fabre's, 135

Faulkner's, 135

first publicly described, 7, 17

for rapid working, 195

Gaiser's, 253

Guillemin's, 135

Henry's, 27

Hjorth's, 224

horseshoe, 49, 188

Hughes', 195, 267

in Bell's telephone, 135

invented in 1825, 16

iron-clad, 50, 78, 133, 135, 188

Jensen's, 191

INDEX.

Electromagnet, Joule's, 39, 46

law of, 8

long vs. short limbs, 154

of Brush arc lamp, 207

Radford's, 46

Roberts', 46

RolofTs, 254

Romershausen's, 135

RuhmkorfTs, 204

Smith's, 253

Stevens and Hard}', 252

Sturgeon's, 18

Varley's, 188, 202

Wagoner's, 204

without iron, 251
Electromagnetic clutch, 273

engines, 223

inertia, 187, 208

mechanism, 222, 270

pop-gun, 205

repulsion, 208

tools, 277

vibrators, 274
Electromagnets, diminutive, 100

fallacies and facts about, 77

for alternating currents, 206

for arc lamp (see arc lamp
mechanism)

for lifting, 52

for maximum range of attrac-
tion, 203

for maximum traction, 03

for minimum weight, 203

formulae for, 74

for quickest action, 209

for traction, 41, 52

heating of, 76

in telegraph apparatus, 207, 221

saturation of, 44

specifications of, 185

to produce rapid vibrations, 53

with iron between the windings,
208

with long versus short limbs, 79,
171, 220

Elphinstone, Lord, application of
magnetic circuit in dynamo design,
12

Equalizing the pull of a magnet, 258
Ewing, curves of magnetization, 57
hysteresis, 75

maximum magnetization, 72
measurement of permeability,

59, 63
on effect of joints, 155

FABRE, iron-clad electromagnet,
135
Faraday, lines of force, 11

rotation of permanent magnet,

16
Faulkner, iron-clad electromagnet,

135

Forbes, electromagnetic brake, 272
formulae for estimation of leak-
age, 144

magnetic leakage, 13
polarized apparatus, 269
Frolich, law of the electromagnet, 73
Froment s equalizer, 260
vibrating mechanism, 274

AISER'S electromagnet, 253
Galvanometer coils, 270

VJT

Gauss, magnetic measurements, 113
Gloesner, polarized magnets, 266
Grove, range of action, 225
Guillemin, iron-clad electromagnet,
135

TT ACKER'S rule for traction, 98
*"* Hankel, magnetism of long

bars, 152
Hankel, working of coil-and-plunger,

242
Heating of magnet coils, 96, 98, 173,

174, 175, 176, 183, 204, 207, 208, 257
Heaviside, magnetic reluctance, 82
Helmholtz, law regarding inter-
rupted currents, 8

"284

INDEX.

Henry's first experiments, 27
Hjorth's electromagnet, 224

polarized magnets, 266
Hopkinson, curves of magnetization,
65

design of dynamos, 13

maximum magnetization, 72

measurement of permeability,

59, 63

Horseshoe electromagnet, 49
Houdin's equalizer, 262
Hughes, distance between poles, 194

magnetic balance, 59

polarized magnet, 267

printing telegraph magnets, 194,

196

Hunt, range of action of electromag-
nets, 224
Hysteresis, 75

viscous, 77

IRON-CLAD electromagnet, 50, 78,
133, 135

range of action, 249
Iron, magnetic qualities affected by

hammering, rolling, etc., 77
maximum magnetization of, 92
permeability of. 92
permeability of, compared with

air, 85, 118
the magnetic properties of , 54, 56

TENSEN'S electromagnet, 191
J indicator, 275
Joints, effect of, on magnetic reluc-
tance, 155
Joule, experiment with Sturgeon's

magnet, 20

lamination of cores, 207
law of mutual attraction, 40
law of traction, 100
length of electromagnet, 94
magnetic saturation, 56
maximum magnetization, 72

Joule, maximum power of an elec-
tromagnet, 11

range of action, 225

researches, 39, 81

results of traction experiments,
91

tubular cores, 158

TT^APP, design of dynamos, 13
-**. maximum magnetization, 72
Keeper, effect of position on tractive

power, 78
effect of removing suddenly, 78,

202

Kirchhoff, measurement of permea-
bility, 59

Krizik, coned and cylindrical plung-
ers, 247

T- ANGDON-DAVIES' rate gover-
M nor, 275

suppression of sparking. 279
Laplace, two magnetic fluids, 9
Law of inverse squares, 13, 78, 110,
112, 226, 251

a point law, 111

apparatus to illustrate, 113, 115

defined, 111

Law of the electromagnet, 73
Law of the magnetic circuit, applied
to traction, 87

as stated by Maxwell, 88

explanation of symbols, 82
Law of Helmholtz, 209
Law of traction, 71, 100, 101, 102

verified, 90
Leakage of magnetic lines, 85, 1 8,

110, 112, 129

Leakage reluctances, 148
Lemont, law of the electromagnet, 73
Lenz, magnetism of long bars, 151
Leupold, winding for range of ac-
tion, 248

Lines of force, 11, 55
Lyttle's patent for winding, 184

INDEX.

285

MAGNETIC adherence, 271
balance of Prof. Hughes, 59
brake, 272

centre of gravity, 112, 113
circuit, 10,11, 12, 13,47

application of, in dynamo de-
sign, 12, 13

for greatest traction, 97
formulae for, 86, 87, 101, 102
tendency to become more

compact, 123, 204
various parts of, 49
conductivity, 10, 11, 83
field, action of, on small iron

sphere, 255

flux, calculation of, 83, 164
gear, 271
insulation, 84
leakage, 13

calculation of, 122, 161
calculation of coefficient, 168
coefficient of, "v, 11 145
due to air-gaps, 120, 144
estimation of, 144, 150, 169
measurement of, 137 [193
proportional to the surface,
relation of, to pull, 139
memory, 172, 221
moments, 13, 87, 158
output of electromagnets, 185
permeability, 11, 54, 83
polarity, rule for determining, 51
pole of the earth, 113
reluctance, calculation of, 3, 95,

165

of divided iron ring, 117
of iron ring, 117
of waste and stray field, for-
mulae for, 146, 150
resistance, 12, 82
saturation, 47, 56, 58
shunts, 13
Magnetism, free, 9

of long iron bars, 151
Magnetization and magnetic traction,
tabular data, 89

Magnetization, calculation of, 161, 164

defined, 87

internal, 9, 54

internal distribution of, 63, 78, 138

of different materials, 57

surface, 9, 13, 48
Magnetometer, 114
Magneto-motive force, 11, 12, 81

calculation of, 82, 83
Maikoff and De Kabath, repulsion

mechanism, 274
Marsh, first vibrating mechanism, 274

vibrating pendulum, 16
Maxwell, galvanometer, 270

law of the magnetic circuit
stated, 88

law regarding circulation of al-
ternating currents, 8

magnetic conductivity, 11
Mirand, inventor of the electric bell,

274

Mitis metal, magnetization of, 72
Moll's experiments, 22, 34
Moseley's indicator, 275
Mttller, law of the electromagnet, 73

magnetism of long bars, 152

measurement of permeability, 58

NEEF, vibrating mechanism, 274
Newton's signet ring load-
stone, 100
Nickles, classification of magnets,

188

distance between limbs of horse-
shoe magnet s, 158
distance between poles, 194
length of armatures, 158
magnetic brake, 272
magnetic gear, 271
traction affected by extent of

polar surface, 104
tubular cores, 158

approach, 258, 263
Oersted's discovery, 16
Ohm's law, 8, 12, 26, 81, 209

286

INDEX.

PAGE, electric motor, 256
sectioned coils, 256
electromagnetic engine, 223
Paine, sheath for magnets, 278
Permanent magnets contrasted with

electromagnets, 199
uses of, 264
Permeability, calculation of, 163

methods of measuring, 58
Permeameter, 70
Permeance, of telegraph instrument

magnets, 150

Perry, magnetic shunts, 13
Pfaff , tubular cores, 158
Plungers, coned vs. cylindrical, 247

of iron and steel, 244
Point poles, 114, 115

action of single coil on, 230
Poisson, two magnetic fluids, 9
Polar distribution of magnetic lines,

137

region, defined, 112, 113
Polarized apparatus for indicators,

276

mechanism, 264

Pole-pieces, convex versus flat, 79, 104
Dub's experiments with, 126
Du Moncel's experiments with,

132
effect of position on tractive

power, 79

effect on lifting power, 78
on horseshoe magnets, 198
Poles, effect of distance between, 194

flat vs. pointed, 125, 127
Preece, self-induction in relays, 218
winding of coils, 184

IT) adford's electromagnet, 46
-*- ^ Range of action of electromag-
nets, 224, 225, 248
Rate governor, 275
Reluctance, 12, 82
Repulsion mechanism, 273
Residual magnetism, 67

Resistance of electromagnet and
battery, 185

of insulated wire, rule for, 176
Ritchie, magnetic circuit, 10

steel magnets, 172
Roberts 1 electromagnet, 46
Robertson, galvanometer, 270
Roloff s electromagnet, 254
Romershausen, iron-clad electro : n ag-

net, 135

Rowan, electromagnetic tools, 277
Rowland, analogy of magnetic and

electric circuits, 12

first statement of the law of the
magnetic circuit, 81

magnetic permeability, 11

maximum magnetization, 72

measurement of permeability,

59, 63
Ruhmkorff 's electromagnet, 204

O ATURATION, curve of, 153

distribution of, 138
effect of, on permeability, 118
Schweigger's multiplier, 16, 28
Sectioned coils with plunger, 256
Self-induction, effect of, 217

in telegraph magnets, 214, 218
Siemens, differential coil-and-plung-

er, 250
relay, 270

Siphon recorder, 270
Smith, plunger electromagnet, 253
Sparking, suppression of, 277
Steel, magnetization of, 58

permeability of, 61
Stephenson, electric motors not

practicable, 225

Stevens and Hardy, plunger electro-
magnet, 252

Stowletow, measurement of permea-
bility, 59

Sturgeon, biographical sketch, 17
experiments on bar magnets, 125
experiments on leakage, 122

INDEX.

287

Sturgeon, first description of electro-
magnet, 7, 17

magnetic circuit, 10

polar extensions j 132

polarized apparatus, 266

portrait wanted, 27 9

tubular cores, 158
Sturgeon's apparatus lost, 20

first electromagnet, 18

first experiments, 20
Surface magnetism, 108, 109

r MIME-CONST ANT of electric cir-

- cuit, 211, 213, 216, 218
Thomas, wire gauge table, 178
Thomson (Elihu), electromagnetic

phenomena, 208

(J J.), on effect of joints, 155

(Sir Wm.), current meters, 255

polarized magnets, 266

range of action, 225

rule for winding electromagnets,
188

siphon recorder, 270

winding galvanometer coils, 257
Thorpe's semaphore indicator, 275
Traction, formula for, 98

in terms of weight of magnet, 98
Tractive power of magnets affected
by surface contact, 135, 151

integral formula for, 89
Treve, iron wire coil, 248
Tubular coils, action of, on a unit
pole, 232

attraction between, 243

winding of, 256

Two magnetic fluids, doctrine of, 9
Tyndall, range of action, 225

V

ARLEY, copper sheath for mag-

net coils, 27H
electromagnet, 202
iron-clad electromagnet, 188

Varley, polarized magnets, 266
Vaschy, coefficients of self-induc-
tion, 218
Vibrators, 274

Vincent, application of magnetic cir-
cuit in dynamo design, 12
Viscous hysteresis, 77
Von Feilitzsch, plungers of iron and

steel, 244

magnetism of long bars, 152
measurement of permeability, 59
tubular cores, 158
Von Koike, distribution or magnetic

lines, 137

Von Waltenhofen, attraction of two
tubular coils, 243

WAGENER'S electromagnet, 204
Wagner, vibrating mechan-
ism, 274
Walmsley, magnetic reluctance of

air, 148
Wheatstone, Henry's visit to, 38

equalizer for telegraph instru-
ment, 264

oblique approach, 259
polarized apparatus, 266
Winding a magnet in sections, 256
calculation of, 95, 173, 183, 190
coils in multiple arc, 258
differential, 278

effect of, on range of action, 248
for constant pressure and for

constant current, 182
iron vs. copper wire, 202
of tubular coils, 256
position of coils, 193
size of coils, 191
thick versus thin wire, 78
wire of graduated thickness, 257
Wire gauge and ampereage table,

178

Wrought iron, magnetization of, 56,
. 64,65

557f>94

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